Citation: Ramón Delanoy, Misael Díaz-Asencio, Rafael Méndez-Tejeda. Sedimentation in the Bay of Samaná, Dominican Republic (1900–2016)[J]. AIMS Geosciences, 2020, 6(3): 298-315. doi: 10.3934/geosci.2020018
[1] | Ruma Qamar, Tabinda Nahid, Mumtaz Riyasat, Naresh Kumar, Anish Khan . Gould-Hopper matrix-Bessel and Gould-Hopper matrix-Tricomi functions and related integral representations. AIMS Mathematics, 2020, 5(5): 4613-4623. doi: 10.3934/math.2020296 |
[2] | Shahid Mubeen, Rana Safdar Ali, Iqra Nayab, Gauhar Rahman, Thabet Abdeljawad, Kottakkaran Sooppy Nisar . Integral transforms of an extended generalized multi-index Bessel function. AIMS Mathematics, 2020, 5(6): 7531-7547. doi: 10.3934/math.2020482 |
[3] | Rupak Datta, Ramasamy Saravanakumar, Rajeeb Dey, Baby Bhattacharya . Further results on stability analysis of Takagi–Sugeno fuzzy time-delay systems via improved Lyapunov–Krasovskii functional. AIMS Mathematics, 2022, 7(9): 16464-16481. doi: 10.3934/math.2022901 |
[4] | D. L. Suthar, A. M. Khan, A. Alaria, S. D. Purohit, J. Singh . Extended Bessel-Maitland function and its properties pertaining to integral transforms and fractional calculus. AIMS Mathematics, 2020, 5(2): 1400-1410. doi: 10.3934/math.2020096 |
[5] | Won-Kwang Park . On the application of subspace migration from scattering matrix with constant-valued diagonal elements in microwave imaging. AIMS Mathematics, 2024, 9(8): 21356-21382. doi: 10.3934/math.20241037 |
[6] | Fethi Bouzeffour . Inversion formulas for space-fractional Bessel heat diffusion through Tikhonov regularization. AIMS Mathematics, 2024, 9(8): 20826-20842. doi: 10.3934/math.20241013 |
[7] | Yongjian Hu, Huifeng Hao, Xuzhou Zhan . On the solvability of the indefinite Hamburger moment problem. AIMS Mathematics, 2023, 8(12): 30023-30037. doi: 10.3934/math.20231535 |
[8] | Hasan Gökbaş . Some properties of the generalized max Frank matrices. AIMS Mathematics, 2024, 9(10): 26826-26835. doi: 10.3934/math.20241305 |
[9] | Mohamed Obeid, Mohamed A. Abd El Salam, Mohamed S. Mohamed . A novel generalized symmetric spectral Galerkin numerical approach for solving fractional differential equations with singular kernel. AIMS Mathematics, 2023, 8(7): 16724-16747. doi: 10.3934/math.2023855 |
[10] | Yunbo Tian, Sheng Chen . Prime decomposition of quadratic matrix polynomials. AIMS Mathematics, 2021, 6(9): 9911-9918. doi: 10.3934/math.2021576 |
In the last few decades, the investigation of fractional differential equations has been picking up much attention of researchers. This is due to the fact that fractional differential equations have various applications in engineering and scientific disciplines, for example, fluid dynamics, fractal theory, diffusion in porous media, fractional biological neurons, traffic flow, polymer rheology, neural network modeling, viscoelastic panel in supersonic gas flow, real system characterized by power laws, electrodynamics of complex medium, sandwich system identification, nonlinear oscillation of earthquake, models of population growth, mathematical modeling of the diffusion of discrete particles in a turbulent fluid, nuclear reactors and theory of population dynamics. The fractional differential equation is an important tool to describe the memory and hereditary properties of various materials and phenomena. The details on the theory and its applications may be found in books [35,38,40,42] and references therein.
It has also been many subjects in fractional calculus that have been developed in various fields, from pure mathematical theory to applied sciences such as modeling of heat transfer in heterogeneous media [43], modeling of ultracapacitor and beams heating [25], etc. These applications are mainly due to the fact that many physical systems are related to fractional-order dynamics and their behaviors are governed by fractional differential equations (FDEs) [39]. The significant importance of using FDEs describes the non-local property [31], which means the current state and all its previous states affect the next state of a dynamical system. We remind that an essential issue about fractional calculus problems is difficult in obtaining analytical solutions. Therefore, numerical and approximation methods are commonly proposed to obtain approximate solutions for this kind of problems, e.g., [8,9,10,28,32,33,41].
Recently, fractional-order differential equations equipped with a variety of boundary conditions have been studied. The literature on the topic includes the existence and uniqueness results related to classical, initial value problem, periodic/anti-periodic, nonlocal, multi-point, integral boundary conditions, and Integral Fractional Boundary Condition, for instance, the monographs of Ahmed et al. [4], Benchohra et al. [13], W, Benhamida et al. [16], D. Chergui et al. [23], Chen et al. [24], Goodrich et al. [29] and Zhang et al. [47].
On the other hand, the nonlocal problem has been studied by many authors. The existence of a solution for abstract Cauchy differential equations with nonlocal conditions in a Banach space has been considered first by Byszewski [19]. In physical science, the nonlocal condition may be connected with better effect in applications than the classical initial condition since nonlocal conditions are normally more exact for physical estimations than the classical initial condition. For the study of nonlocal problems, we refer to [20,21,22,26,27,29,47] and references given therein.
This paper deals with the existence of solutions to the boundary value problem for fractional-order differential equations:
CDrx(t)=f(t,x(t)),t∈J:=[1,T],0<r≤1, | (1.1) |
with fractional boundary condition:
αx(1)+βx(T)=λIqx(η)+δ,q∈(0,1]. | (1.2) |
where Dr is the Caputo-Hadamard fractional derivative, 0<r<1, 0<q≤1, and let E be a Banach space space with norm ‖.‖, f:J×E→E is given continuous function and satisfying some assumptions that will be specified later. α,β,λ are real constants, and η∈(1,T), δ∈E.
In this paper, we present existence results for the problem (1.1)-(1.2) using a method involving a measure of noncompactness and a fixed point theorem of Mönch type. that technique turns out to be a very useful tool in existence for several types of integral equations; details are found in A. Aghajani et al. [3], Akhmerov et al. [5], Alvàrez [6], et al. [11,12], Benchohra et al. [14,15], Guo et al. [30], Mönch [37], Szufla [44]. We can use a numerical method to solve the problem in Equation (1.1-1.2), for instance, see [8,9,10,28,32,33,41].
The organization of this work is as follows. In Section 2, we introduce some notations, definitions, and lemmas that will be used later. Section 3 treats the existence of solutions in Banach spaces. In Section 4, we illustrate the obtained results by an example. Finally, the paper concludes with some interesting observations in Section 5.
In what follows we introduce definitions, notations, and preliminary facts which are used in the sequel. For more details, we refer to [1,2,5,11,35,36,42,44].
Denote by C(J,E) the Banach space of continuous functions x:J→E, with the usual supremum norm
‖x‖∞=sup{‖x(t)‖,t∈J}. |
Let L1(J,E) be the Banach space of measurable functions x:J→E which are Bochner integrable, equipped with the norm
‖x‖L1=∫J|x(t)|dt. |
Let the space
ACnδ([a,b],E)={h:[a,b]→R:δn−1h(t)∈AC([a,b],E)}. |
where δ=tddt is the Hadamard derivative and AC([a,b],E) is the space of absolutely continuous functions on [a,b].
Now, we give some results and properties of fractional calculus.
Definition 2.1. (Hadamard fractional integral) (see [35])
The left-sided fractional integral of order α>0 of a function y:(a,b)→R is given by
Iαa+y(t)=1Γ(α)∫ta(logts)α−1y(s)dss | (2.1) |
provided the right integral converges.
Definition 2.2. (Hadamard fractional derivative) (see [35])
The left-sided Hadamard fractional derivative of order α≥0 of a continuous function y:(a,b)→R is given by
Dαa+f(t)=δnIn−αa+y(t)=1Γ(n−α)(tddt)n∫ta(logts)n−α−1y(s)dss | (2.2) |
where n=[α]+1, and [α] denotes the integer part of the real number α and δ=tddt.
provided the right integral converges.
There is a recent generalization introduced by Jarad and al in [34], where the authors define the generalization of the Hadamard fractional derivatives and present properties of such derivatives. This new generalization is now known as the Caputo-Hadamard fractional derivatives and is given by the following definition:
Definition 2.3. (Caputo-Hadamard fractional derivative) (see [34,46])
Let α=0, and n=[α]+1. If y(x)∈ACnδ[a,b], where 0<a<b<∞ and
ACnδ([a,b],E)={h:[a,b]→R:δn−1h(t)∈AC([a,b],E)}. |
The left-sided Caputo-type modification of left-Hadamard fractional derivatives of order α is given by
CDαa+y(t)=Dαa+(y(t)−n−1∑k=0δky(a)k!(logts)k) | (2.3) |
Theorem 2.4. (See [34])
Let α≥0, and n=[α]+1. If y(t)∈ACnδ[a,b], where 0<a<b<∞. Then CDαa+f(t) exist everywhere on [a,b] and
(i) if α∉N−{0}, CDαa+f(t) can be represented by
CDαa+y(t)=In−αa+δny(t)=1Γ(n−α)∫ta(logts)n−α−1δny(s)dss | (2.4) |
(ii) if α∈N−{0}, then
CDαa+y(t)=δny(t) | (2.5) |
In particular
CD0a+y(t)=y(t) | (2.6) |
Caputo-Hadamard fractional derivatives can also be defined on the positive half axis R+ by replacing a by 0 in formula (2.4) provided that y(t)∈ACnδ(R+). Thus one has
CDαa+y(t)=1Γ(n−α)∫ta(logts)n−α−1δny(s)dss | (2.7) |
Proposition 2.5. (see [34,35])
Let α>0,β>0,n=[α]+1, and a>0, then
Iαa+(logta)β−1(x)=Γ(β)Γ(β−α)(logxa)β+α−1CDαa+(logta)β−1(x)=Γ(β)Γ(β−α)(logxa)β−α−1,β>n,CDαa+(logta)k=0,k=0,1,...,n−1. | (2.8) |
Theorem 2.6. (see [45])
Let y(t)∈ACnδ[a,b],0<a<b<∞ and α≥0,β≥0, Then
CDαa+(Iαa+y)(t)=(Iβ−αa+y)(t),CDαa+(CDβa+y)(t)=(CDα+βa+y)(t). | (2.9) |
Lemma 2.7. (see [34])
Let α≥0, and n=[α]+1. If y(t)∈ACnδ[a,b], then the Caputo-Hadamard fractional differential equation
CDαa+y(t)=0 | (2.10) |
has a solution:
y(t)=n−1∑k=0ck(logta)k | (2.11) |
and the following formula holds:
Iαa+(CDαa+y)(t)=y(t)+n−1∑k=0ck(logta)k | (2.12) |
where ck∈R,k=1,2,...,n−1
Now let us recall some fundamental facts of the notion of Kuratowski measure of noncompactness.
Definition 2.8. ([5,11]) Let E be a Banach space and ΩE the bounded subsets of E. The Kuratowski measure of noncompactness is the map μ:ΩE→[0,∞] defined by
μ(B)=inf{ϵ>0:B⊆∪ni=1Bi and diam(Bi)≤ϵ}; here B∈ΩE. |
This measure of noncompactness satisfies some important properties [5,11]:
(a) μ(B)=0⇔¯B is compact (B is relatively compact).
(b) μ(B)=μ(¯B).
(c) A⊂B⇒μ(A)≤μ(B).
(d) μ(A+B)≤μ(A)+μ(B)
(e) μ(cB)=|c|μ(B);c∈R.
(f) μ(convB)=μ(B).
Here ¯B and convB denote the closure and the convex hull of the bounded set B, respectively. The details of μ and its properties can be found in ([5,11]).
Definition 2.9. A map f:J×E→E is said to be Caratheodory if
(ⅰ) t↦f(t,u) is measurable for each u∈E;
(ⅱ) u↦F(t,u) is continuous for almost all t∈J.
Notation 2.10. for a given set V of functions v:J→E, let us denote by
V(t)={v(t):v∈V},t∈J, |
and
V(J)={v(t):v∈V,t∈J}. |
Let us now recall Mönch's fixed point theorem and an important lemma.
Theorem 2.11. ([2,37,44]) Let D be a bounded, closed and convex subset of a Banach space such that 0∈D, and let N be a continuous mapping of D into itself. If the implication
V=¯convN(V) or V=N(V)∪0⇒μ(V)=0
holds for every subset V of D, then N has a fixed point.
Lemma 2.12. ([44]) Let D be a bounded, closed and convex subset of the Banach space C(J,E), G a continuous function on J×J and f a function from J×E⟶E which satisfies the Caratheodory conditions, and suppose there exists p∈L1(J,R+) such that, for each t∈J and each bounded set B⊂E, we have
limh→0+μ(f(Jt,h×B))≤p(t)μ(B); here Jt,h=[t−h,t]∩J. |
If V is an equicontinuous subset of D, then
μ({∫JG(s,t)f(s,y(s))ds:y∈V})≤∫J‖G(t,s)‖p(s)μ(V(s))ds. |
This section is devoted to the existence results for problem (1.1)-(1.2).
Definition 3.1. A function x∈AC1δ(J,E) is said to be a solution of the problem (1.1)-(1.2) if x satisfies the equation CDrx(t)=f(t,x(t)) on J, and the conditions (1.2).
For the existence of solutions for the problem (1.1)-(1.2), we need the following auxiliary lemma.
Lemma 3.2. Let h:[1,T)→E be a continuous function. A function x is a solution of the fractional integral equation
x(t)=Irh(t)+1Λ{λIr+qh(η)−βIrh(T)+δ} | (3.1) |
if and only if x is a solution of the fractional BVP
CDrx(t)=h(t),t∈J,r∈(0,1] | (3.2) |
αx(1)+βx(T)=λIqx(η)+δ,q∈(0,1] | (3.3) |
Proof. Assume x satisfies (3.2). Then Lemma 2.8 implies that
x(t)=Irh(t)+c1. | (3.4) |
The condition (3.3) implies that
x(1)=c1 |
x(T)=Irh(T)+c1 |
Iqx(1)=Ir+qh(η))+c1(logη)qΓ(q+1) |
So
αc1+βIrh(T)+βc1=λIr+qh(η))+c1λ(logη)qΓ(q+1)+δ |
Thus,
c1(α+β−λ(logη)qΓ(q+1))=λIr+qh(η))−βIrh(T)+δ. |
Consequently,
c1=1Λ{λIr+qh(η))−βIrh(T)+δ}. |
Where,
Λ=(α+β−λ(logη)qΓ(q+1)) |
Finally, we obtain the solution (3.1)
x(t)=Irh(t)+1Λ{λIr+qh(η)−βIrh(T)+δ} |
In the following, we prove existence results, for the boundary value problem (1.1)-(1.2) by using a Mönch fixed point theorem.
(H1) f:J×E→E satisfies the Caratheodory conditions;
(H2) There exists p∈L1(J,R+)∩C(J,R+), such that,
‖f(t,x)‖≤p(t)‖x‖, for t∈J and each x∈E; |
(H3) For each t∈J and each bounded set B⊂E, we have
limh→0+μ(f(Jt,h×B))≤p(t)μ(B);hereJt,h=[t−h,t]∩J. |
Theorem 3.3. Assume that conditions (H1)-(H3) hold. Let p∗=supt∈Jp(t). If
p∗M<1 | (3.5) |
With
M:={(logT)rΓ(r+1)+|λ|(logη)r+q|Λ|Γ(r+q+1)+|β|(logT)r|Λ|Γ(r+1)} |
then the BVP (1.1)-(1.2) has at least one solution.
Proof. Transform the problem (1.1)-(1.2) into a fixed point problem. Consider the operator F:C(J,E)→C(J,E) defined by
Fx(t)=Irh(t)+1Λ{λIr+qh(η)−βIrh(T)+δ} | (3.6) |
Clearly, the fixed points of the operator F are solutions of the problem (1.1)-(1.2). Let
R≥|δ||Λ|(1−p∗M). | (3.7) |
and consider
D={x∈C(J,E):‖x‖≤R}. |
Clearly, the subset D is closed, bounded and convex. We shall show that F satisfies the assumptions of Mönch's fixed point theorem. The proof will be given in three steps.
Step 1: First we show that F is continuous:
Let xn be a sequence such that xn→x in C(J,E). Then for each t∈J,
‖(Fxn)(t)−(Fx)(t)‖≤1Γ(r)∫t1(logts)r−1‖f(s,xn(s))−f(s,x(s))‖dss+|λ||Λ|Γ(r+q)∫η1(logηs)r+q−1‖f(s,xn(s))−f(s,x(s))‖dss+|β||Λ|Γ(r)∫T1(logTs)r−1‖f(s,xn(s))−f(s,x(s))‖dss≤{(logT)rΓ(r+1)+|λ|(logη)r+q|Λ|Γ(r+q+1)+|β|(logT)r|Λ|Γ(r+1)}‖f(s,xn(s))−f(s,x(s))‖ |
Since f is of Caratheodory type, then by the Lebesgue dominated convergence theorem we have
‖F(xn)−F(x)‖∞→0 as n→∞. |
Step 2: Second we show that F maps D into itself :
Take x∈D, by (H2), we have, for each t∈J and assume that Fx(t)≠0.
‖(Fx)(t)‖≤1Γ(r)∫t1(logts)r−1‖f(s,x(s))‖dss+|λ||Λ|Γ(r+q)∫η1(logηs)r+q−1‖f(s,x(s))‖dss+|β||Λ|Γ(r)∫T1(logTs)r−1‖f(s,x(s))‖dss+|δ||Λ|≤1Γ(r)∫t1(logts)r−1p(s)‖x(s)‖dss+|λ||Λ|Γ(r+q)∫η1(logηs)r+q−1p(s)‖x(s)‖dss+|β||Λ|Γ(r)∫T1(logTs)r−1p(s)‖x(s)‖dss+|δ||Λ|≤P∗RΓ(r)∫t1(logts)r−1dss+|λ|P∗R|Λ|Γ(r+q)∫η1(logηs)r+q−1dss+|β|P∗R|Λ|Γ(r)∫T1(logTs)r−1dss+|δ||Λ|≤P∗R{(logT)rΓ(r+1)+|λ|(logη)r+q|Λ|Γ(r+q+1)+|β|(logT)r|Λ|Γ(r+1)}+|δ||Λ|≤P∗RM+|δ||Λ|≤R. |
Step 3: we show that F(D) is equicontinuous :
By Step 2, it is obvious that F(D)⊂C(J,E) is bounded. For the equicontinuity of F(D), let t1,t2∈J, t1<t2 and x∈D, so Fx(t2)−Fx(t1)≠0. Then
‖Fx(t2)−Fx(t1)‖≤1Γ(r)∫t11[(logt2s)r−1−(logt1s)r−1]‖f(s,x(s))‖dss+1Γ(r)∫t2t1(logt2s)r−1‖f(s,x(s))‖dss≤RΓ(r)∫t11[(logt2s)r−1−(logt1s)r−1]p(s)dss+RΓ(r)∫t2t1(logt2s)r−1p(s)dss≤Rp∗Γ(r+1)[(logt2)r−(logt1)r]. |
As t1→t2, the right hand side of the above inequality tends to zero.
Hence N(D)⊂D.
Finally we show that the implication holds:
Let V⊂D such that V=¯conv(F(V)∪{0}). Since V is bounded and equicontinuous, and therefore the function v→v(t)=μ(V(t)) is continuous on J. By assumption (H2), and the properties of the measure μ we have for each t∈J.
v(t)≤μ(F(V)(t)∪{0}))≤μ((FV)(t))≤1Γ(r)∫t1(logts)r−1p(s)μ(V(s))dss+|λ||Λ|Γ(r+q)∫η1(logηs)r+q−1p(s)μ(V(s))dss+|β||Λ|Γ(r)∫T1(logTs)r−1p(s)μ(V(s))dss≤‖v‖Γ(r)∫t1(logts)r−1p(s)dss+|λ|‖v‖|Λ|Γ(r+q)∫η1(logηs)r+q−1p(s)dss+|β|‖v‖|Λ|Γ(r)∫T1(logTs)r−1p(s)dss≤p∗‖v‖{(logT)rΓ(r+1)+|λ|(logη)r+q|Λ|Γ(r+q+1)+|β|(logT)r|Λ|Γ(r+1)}:=p∗‖v‖M. |
This means that
‖v‖(1−p∗M)≤0 |
By (3.5) it follows that ‖v‖=0, that is v(t)=0 for each t∈J, and then V(t) is relatively compact in E. In view of the Ascoli-Arzela theorem, V is relatively compact in D. Applying now Theorem 2.11, we conclude that F has a fixed point which is a solution of the problem (1.1)-(1.2).
Let
E=l1={x=(x1,x2,...,xn,...):∞∑n=1|xn|<∞} |
with the norm
‖x‖E=∞∑n=1|xn| |
We consider the problem for Caputo-Hadamard fractional differential equations of the form:
{D23x(t)=f(t,x(t)),(t,x)∈([1,e],E),x(1)+x(e)=12(I12x(2))+34. | (4.1) |
Here r=23, q=12, δ=34, λ=12, η=2, T=e.
With
f(t,y(t))=t√π−116y(t),t∈[1,e] |
Clearly, the function f is continuous. For each x∈R+ and t∈[1,e], we have
|f(t,x(t))|≤t√π16|x| |
Hence, the hypothesis (H2) is satisfied with p∗=t√π16. We shall show that condition (3.5) holds with T=e. Indeed,
p∗{(logT)rΓ(r+1)+|λ|(logη)r+q|Λ|Γ(r+q+1)+|β|(logT)r|Λ|Γ(r+1)}≃0.6109<1 |
Simple computations show that all conditions of Theorem 3.3 are satisfied. It follows that the problem (4.1) has at least solution defined on [1,e].
In this paper, we obtained some existence results of nonlinear Caputo-Hadamard fractional differential equations with three-point boundary conditions by using a method involving a measure of noncompactness and a fixed point theorem of Mönch type. Though the technique applied to establish the existence results for the problem at hand is a standard one, yet its exposition in the present framework is new. An illustration to the present work is also given by presenting some examples. Our results are quite general give rise to many new cases by assigning different values to the parameters involved in the problem. For an explanation, we enlist some special cases.
● We remark that when λ=0, problem (1.1)-(1.2), the boundary conditions take the form: αx(1)+βx(T)=δ and the resulting problem corresponds to the one considered in [17,18].
● If we take α=q=1, β=0, in (1.2), then our results correspond to the case integral boundary conditions take the form: x(1)=λ∫e1x(s)ds+δ considered in [7].
● By fixing α=1, β=λ=0, in (1.2), our results correspond to the ones for initial value problem take the form:x(1)=δ.
● In case we choose α=β=1, λ=δ=0, in (1.2), our results correspond to periodic/anti-periodic type boundary conditions take the form: x(1)=−(β/α)x(T). In particular, we have the results for anti-periodic type boundary conditions when (β/α)=1. For more details on anti-periodic fractional order boundary value problems, see [45].
● Letting α=1, β=δ=0, in (1.2), then our results correspond to the case fractional integral boundary conditions take the form:x(1)=λIqx(η).
● When, α=β=1, δ=0, in (1.2), our results correspond to fractional integral and anti-periodic type boundary conditions.
In the nutshell, the boundary value problem studied in this paper is of fairly general nature and covers a variety of special cases and we can use a numerical method to solve the problem in equation (1.1-1.2). The possible generalization is to consider the problem (1.1-1.2) on Banach space with another technique, other fixed point theorem and determine the conditions that befit closer to obtain the best results. As another proposal, considering some type of fractional derivative (Hilfer-Hadamard, Hilfer-Katugampola) with respect to another function. we will use the numerical method to solve this problem. These suggestions will be treated in the future.
The authors would like to express their thanks and are grateful to the referees for their helpful comments and suggestions.
The authors declare that there is no conflict of interests regarding the publication of this paper.
[1] |
Delanoy R, Díaz-Asencio M, Méndez-Tejeda R (2019) Effect of Extreme Weather Events on the Sedimentation of the Bay of Samaná, Dominican Republic (1900-2016). J Geogr Geol 11: 56-73. doi: 10.5539/jgg.v11n3p56
![]() |
[2] | Bionini W, Hargraves R, Shagan R (1984) The Caribean-South American Plate Boundary and Regional Tectonic. Geol Soc Am Mem 162. |
[3] | Bird J (1980) Plate Tectonics. Select papers from Publications of American Geophysical Union, 2 Eds., Washington. D.C. |
[4] | Eptisa (2004) Programa SYSMIN. Informe de la unidad hidrogeológica de la península de Samaná. |
[5] |
Dolan J, Mann P, De Zoeten R, et al. (1991) Sedimentologic, stratigraphicand tectonic synthesis of Eocene-Miocene sedimentary basins, Hispañiola and Puerto Rico, In: Mann P, Draper G, Lewis J, Geologic and tectonic development of the North America-Caribbean Plate boundary in Hispañiola. Geological Society of America Special Paper 262: 217-263. doi: 10.1130/SPE262-p217
![]() |
[6] |
Hippensteel SP, Eastin MD, Garcia WJ (2013) The geological legacy of Hurricane Irene: Implications for the fidelity of the paleo-storm record. GSA Today 23: 4-10. doi: 10.1130/GSATG184A.1
![]() |
[7] |
Díaz de Neira JA, Braga JC, Mediato J, et al. (2015) Plio-Pleistocene palaeogeography of the Llanura Costera del Caribe in eastern Hispaniola (Dominican Republic): Interplay of geomorphic evolution and sedimentation. Sediment Geol 325: 90-105. doi: 10.1016/j.sedgeo.2015.05.008
![]() |
[8] | Trefethen JM (1981) Geología para Ingenieros. Décima edición, Cia. Editorial Continental, México. |
[9] |
Brenner M, Binford MW (1988) A sedimentary record of human disturbance from Lake Miragoane, Haiti. J Paleolimnol 1: 85-97. doi: 10.1007/BF00196066
![]() |
[10] | Alonso-Hernández CM, Díaz-Asencio M, Gómez-Batista M, et al. (2016) Radiocronología de sedimentos marinos y su aplicación en la comprensión de los procesos de contaminación ambiental en ecosistemas marinos cubanos. Nucleus 60: 35-40. |
[11] |
Rozanski K, Stichler W, Gonfiantini R et al. (1992) The IAEA 14C Intercomparison exercise 1990. Radiocarbon 34: 506-519. doi: 10.1017/S0033822200063761
![]() |
[12] | Sánchez-Cabeza M, Ruiz-Fernández JA, Díaz-Asencio A (2012) Radiocronología de sedimentos costeros utilizando 210Pb: modelos, validación y aplicaciones. Vienna: IAEA. |
[13] | Salamanca M, Jara B (2003) Distribución y acumulación de plomo (Pb y 210Pb) en sedimentos de los fiordos de la XI región, Chile. Cienc Tecnol Mar 26: 61-71. |
[14] | Rodríguez Vegas E, Gascó Leonarte C, Schmid T, et al. (2014) Estudio Preliminar sobre el uso de los radionúclidos 137Cs y 210Pb y las Técnicas de Espectrorradiometría como Herramientas para determinar el Estado de Erosión de suelos. Inf Téc Ciemat 1297. |
[15] |
Cisternas M, Torres L, Urrutia R, et al. (2000) Comparación ambiental, mediante registros sedimentarios, entre las condiciones prehispánicas y actuales de un sistema lacustre. Rev Chil Hist Nat 73: 151-162 doi: 10.4067/S0716-078X2000000100014
![]() |
[16] | Armstrong-Altrin JS, Botello AV, Villanueva SF, et al. (2019) Geochemistry of surface sediments from the north-western Gulf of Mexico: implications for provenance and heavy metal contamination. Geol Q 63: 522-538. |
[17] | Fourth National Climate Assessment (NCA4) (2018) Available from: https://www.globalchange.gov/nca4. |
[18] | Null J (2017) El Niño and La Niña Years and Intensities. Based on Oceanic Niño Index (ONI), CCM. Available from: https://ggweather.com/enso/oni.htm. |
[19] | Ramón DA, Méndez-Tejeda R (2017) Hydrodynamic Study of Lake Enriquillo in Dominican Republic. J Geosci Environ Prot 5: 115-124. |
[20] |
Ortega-Ariza D, Franseen EK, Santos-Mercado H, et al. (2015) Strontium Isotope Stratigraphy for Oligocene-Miocene Carbonate Systems in Puerto Rico and the Dominican Republic: Implications for Caribbean Processes Affecting Depositional History. J Geol 123: 539-560. doi: 10.1086/683335
![]() |
[21] |
Mercier G, Duchesne J, Blackburn D (2001) Prediction of metal removal efficiency from contaminated soils by physical methods. J Environ Eng 127: 348-358. doi: 10.1061/(ASCE)0733-9372(2001)127:4(348)
![]() |
[22] |
Loring DH, Rantala RTT (1992) Manual for the geochemical analyses of marine sediments and suspended particulate matter. Earth-Sci Rev 32: 235-283. doi: 10.1016/0012-8252(92)90001-A
![]() |
[23] | Díaz de Neira JA, Braga JC, Mediato J, et al. (2017) Evolución paleogeográfica reciente del sector oriental de La Española. Bol Geol Min 128: 675-693. |
[24] |
Anaya-Gregorio A, Armstrong-Altrin JS, Machain-Castillo ML, et al. (2018) Textural and geochemical characteristics of late Pleistocene to Holocene fine-grained deep-sea sediment cores (GM6 and GM7), recovered from southwestern Gulf of Mexico. J Palaeogeogr 7: 253-271. doi: 10.1186/s42501-018-0005-3
![]() |
[25] | Pérez-Estaún A, Hernaiz Huerta PP, Lopera E, et al. (2007) Geología de la República Dominicana: de la construcción de arco-isla a la colisión arco-continente. Bol Geol Min 118: 157-174. |
[26] | Senz JG, Monthel J, Díaz de Neira JA, et al. (2007) La estructura de la Cordillera Oriental de la República. Bol Geol Min 118: 293-311. |
[27] | Hernaiz Huerta PP (2004) Mapa Geológico de la Hoja a E. 1:50.000. 5871-I (La Descubierta) y Memoria correspondiente. Proyecto de Cartografía Geotemática de la República Dominicana. Programa SYSMIN. Dirección General de Minería, Santo Domingo. |
[28] | Meyers PA, Teranes JL (2001) Sediment organic matter. In: Last WM, Smol JP (eds.). Tracking environmental change using lake sediments. Kluwer Academic Publishers, Holanda, 239-269. |
[29] | Rudolph A, Ahumada R, Hernández S (1984) Distribución de la materia orgánica, carbono orgánico, nitrógeno orgánico y fósforo total en los sedimentos recientes de la Bahía Concepción, Chile. Biol Pesq 13: 71-82. |
[30] | Rodríguez L, Jiménez A, Grau A (1996) Separación del 210Pb, 210Bi y 210Po mediante columna de cambio iónico y su calibración por centelleo líquido. Ciemat 27: 1-30. |
[31] | Lozano RL, San Miguel EG, Bolívar JP (2011) Assessment of the influence of in situ 210Bi in the calculation of in situ 210Po in air aerosols: Implications on residence time calculations using 210Po/210Pb activity ratios. J Geophys Res 116: D08206. |
[32] | Mosqueda Peña F (2010) Desarrollo de procedimientos para la determinación de radioisótopos en muestras ambientales mediante técnicas de bajo recuento por centelleo líquido y radiación Cerenkov. Universidad de Huelva. Tesis Doctoral. |
[33] | IAEA (1989) Isotopes of Noble gases as tracers in environmental studies. Proceeding Consultants Meeeting, Agency International, Vienna. |
[34] | Buchman MF (1999) NOAA Screening Quick Reference Tables. In: National Oceanic and Atmospheric Administration, NOAA HAZMAT Report, Seattle WA, Coastal protection and restoration division, 12. |
[35] | Rudnick RL, Gao S (2003) Composition of the Continental Crust. In: Rudnick RL, Treatise on Geochemistry 3: 1-64. |
[36] |
Choueri RB, Cesar A, Torres RJ, et al. (2009) Integrated sediment quality assessment in Paranaguá Estuarine System, Southern Brazil. Ecotoxicol Environ Saf 72: 1824-1831. doi: 10.1016/j.ecoenv.2008.12.005
![]() |
[37] |
Zhang X, Man X, Jiang H (2015) Spatial distribution and source analysis of heavy metals in the marine sediments of Hong Kong. Environ Monit Assess 187: 1-12. doi: 10.1007/s10661-014-4167-x
![]() |
[38] |
Pourabadehei M, Mulligan CN (2016) Effect of the resuspension technique on distribution of the heavy metals in sediment and suspended particulate matter. Chemosphere 153: 58-67. doi: 10.1016/j.chemosphere.2016.03.026
![]() |
[39] |
Dou Y, Li J, Zhao J, et al. (2013) Distribution, enrichment and source of heavy metals in surface sediments of the eastern Beibu Bay, South China Sea. Mar Pollut Bull 67: 137-145. doi: 10.1016/j.marpolbul.2012.11.022
![]() |
[40] |
Pejman A, Bidhendi GN, Ardestani M, et al. (2015) A new index for assessing heavy metals contamination in sediments: A case study. Ecol Indic 58: 365-373. doi: 10.1016/j.ecolind.2015.06.012
![]() |
[41] | Dolan JF, Mann P (1998) Active Strike-slip and Collisional Tectonics of the Norther Caribbean Plate Boundary Zone. Department of Earth Sciences University Southern of California. The Geological Society of America. Special Paper 326. |
[42] |
Mann P, Burke K, Matumoto T (1984) Neotectonics of Hispañiola: plate motion, sedimentation, and seismicity at a restraining bend. Earth Planet Sci Lett 70: 311-324. doi: 10.1016/0012-821X(84)90016-5
![]() |
[43] | Fernández-Domingo JI (2010) Los Tesoros del Mar y su Régimen Jurídico. Biblioteca Iberoamericana de Derecho, Madrid, Buenos Aires. |