
AIMS Mathematics, 2019, 4(4): 11011113. doi: 10.3934/math.2019.4.1101
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Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions
Faculty of Sciences and Technology, Department of Mathematics and Informatics, University of Souk Ahras, P. O. Box 1553, Souk Ahras, 41000, Algeria
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References
1.S. Zhang, The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl., 252 (2000), 804812.
2.Z. Bai, H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311 (2005), 495505.
3.M. Matar, On existence of positive solution for initial value problem of nonlinear fractional differential equations of order 1 < α ≤ 2, Acta Mathematica Universitatis Comenianae, 84 (2015), 5157.
4.M. Xu, Z. Han, Positive solutions for integral boundary value problem of twoterm fractional differential equations, Bound. Value Probl.,2018 (2018), 100.
5.M. Benchohra, J. E. Lazreg, Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative, Studia Universitatis BabesBolyai Matematica, 62 (2017), 2738.
6.B. Ahmad and S. K. Ntouyas, Existence and uniqueness of solutions for CaputoHadamard sequential fractional order neutral functional differential equations, Electronic Journal of Differential Equations, 2017 (2017), 111.
7.Z. Bai, T. T. Qiu, Existence of positive solution for singular fractional differential equation, Appl. Math. Comput., 215 (2009), 27612767.
8.H. Boulares, A. Ardjouni, Y. Laskri, Positive solutions for nonlinear fractional differential equations, Positivity, 21 (2017), 12011212.
9.D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204 (1996), 609625.
10.E. Kaufmann, E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Electron. J. Qual.Theo., 2008 (2008), 111.
11.C. Kou, H. Zhou, Y. Yan, Existence of solutions of initial value problems for nonlinear fractional differential equations on the halfaxis, Nonlinear AnalTheor, 74 (2011), 59755986.
12.C. Wang, R. Wang, S. Wang, et al. Positive solution of singular boundary value problem for a nonlinear fractional differential equation, Bound. Value Probl., 2011 (2011), 297026.
13.C. Wang, H. Zhang, S. Wang, Positive solution of a nonlinear fractional differential equation involving Caputo derivative, Discrete Dyn. Nat. Soc., 2012 (2012), 425408.
14.M. Xu, S. Sun, Positivity for integral boundary value problems of fractional differential equations with two nonlinear terms, J. Appl. Math.Comput., 59 (2019), 271283.
15.S. Zhang, Existence results of positive solutions to boundary value problem for fractional differential equation, Positivity, 13 (2009), 583599.
16.A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 2006.
17.K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, New York, 1993.
18.I. Podlubny, Fractional differential equations, Academic Press,San Diego, 1999.
19.A. Jannelli, M. Ruggieri and M. P. Speciale, Analytical and numerical solutions of time and space fractional advectiondiffusionreaction equation, Commun. Nonlinear Sci., 70 (2019), 89101.
20.A. Jannelli, M. Ruggieri and M. P. Speciale, Exact and numerical solutions of timefractional advectiondiffusion equation with a nonlinear source term by means of the Lie symmetries, Nonlinear Dynamics, 92 (2018), 543555.
21.D. R. Smart, Fixed point theorems, Cambridge Uni. Press, Cambridge, 1980.
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