
AIMS Mathematics, 2020, 5(1): 259272. doi: 10.3934/math.2020017
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
CaputoHadamard fractional differential equation with threepoint boundary conditions in Banach spaces
1 Laboratory of Mathematics and Applied Sciences University of Ghardaia, 47000, Algeria
2 Faculty of Sciences and Technology, Saad Dahlab University, Blida, Algeria
Received: , Accepted: , Published:
References
1. R. P. Agarwal, M. Benchohra, D. Seba, On the application of measure of noncompactness to the existence of solutions for fractional differential equations, Results Math., 55 (2009), 221230.
2. R. P. Agarwal, M. Meehan, D. O'Regan, Fixed Point Theory and Applications, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 2001.
3. A. Aghajani, A. M. Tehrani, D. O'Regan, Some New Fixed Point Results via the Concept of Measure of Noncompactness, Filomat, 29 (2015), 12091216.
4. R. P. Agarwal, B. Ahmad, A. Alsaedi, Fractionalorder differential equations with antiperiodic boundary conditions: a survey, Bound. Value Probl., 2017 (2017), 127.
5. R. R. Akhmerov, M. I. Kamenskii, A. S. Patapov, et al. Measures of Noncompactness and Condensing Operators, Birkhauser Verlag, Basel, 1992.
6. J. C. Alvàrez, Measure of noncompactness and fixed points of nonexpansive condensing mappings in locally convex spaces, Rev. Real. Acad. Cienc. Exact. Fis. Natur. Madrid, 79 (1985), 5366.
7. A. Ardjouni, A. Djoudi, Positive solutions for nonlinear CaputoHadamard fractional differential equations with integral boundary conditions, Open J. Math. Anal., 3 (2019), 6269
8. P. Assari, S. Cuomo, The numerical solution of fractional differential equations using the Volterra integral equation method based on thin plate splines, Engineering with Computers, 35 (2019), 13911408.
9. P. Assari, M. Dehghan, A meshless local Galerkin method for solving Volterra integral equations deduced from nonlinear fractional differential equations using the moving least squares technique, Appl. Numer. Math., 143 (2019), 276299.
10. P. Assari F. AsadiMehregan, Local radial basis function scheme for solving a class of fractional integrodifferential equations based on the use of mixed integral equations, ZAMMJournal of Applied Mathematics and Mechanics, 99 (2019), 128.
11. J. Banas and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, 1980.
12. J. Banas, M. Jleli, M. Mursaleen, et al. Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness, Springer Nature Singapore, 2017.
13. M. Benchohra, S. Hamani and S. K. Ntouyas, Boundary value problems for differential equations with fractional order, Surveys in Mathematics & its Applications, 3 (2008), 112.
14. M. Benchohra, J. Henderson, D. Seba, Measure of noncompactness and fractional differential equations in Banach spaces, Communications in Applied Analysis, 12 (2008), 419428.
15. M. Benchohra, G. M. N'Guérékata, D. Seba, Measure of noncompactness and nondensely defined semilinear functional differential equations with fractional order, CUBO A Math. J., 12 (2010), 3346.
16. W, Benhamida, J. R. Graef, S. Hamani, Boundary Value Problems for Fractional Differential Equations with Integral and AntiPeriodic Conditions in a Banach Space, Progress in Fractional Differentiation and Applications, 4 (2018), 6570.
17. W. Benhamida, S. Hamani, Measure of Noncompactness and CaputoHadamard Fractional Differential Equations in Banach Spaces, Eurasian Bulletin of Mathematics EBM, 1 (2018), 98106.
18. W. Benhamida, S. Hamani, J. Henderson, Boundary Value Problems For CaputoHadamard Fractional Differential Equations, Advances in the Theory of Nonlinear Analysis and its Applications, 2 (2018), 138145.
19. L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162 (1991), 494505.
20. L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal., 40 (1991), 1119.
21. D. Bahuguna, M. Muslim, Approximation of solutions to nonlocal historyvalued retarded differential equations, Appl. Math. Comput., 174 (2006), 165179.
22. D. Bahuguna, S. Agarwal, Approximations of solutions to neutral functional differential equations with nonlocal history conditions, J. Math. Anal. Appl., 317 (2006), 583602.
23. D. Chergui, T. E. Oussaeif, M. Ahcene, Existence and uniqueness of solutions for nonlinear fractional differential equations depending on lowerorder derivative with nonseparated type integral boundary conditions, AIMS Mathematics, 4 (2019), 112133.
24. T. Chen and W. Liu, An antiperiodic boundary value problem for the fractional differential equations with a pLaplacian operator, Appl. Math. Lett., 25 (2012), 16711675.
25. A. Dzielinski, D. Sierociuk, G. Sarwas, Some applications of fractional order calculus, Bull. Pol. Acad. Sci. Tech. Sci., 58 (2010), 583.
26. F. Li, Gaston M. N' Guérékata, An existence result for neutral delay integrodifferential equations with fractional order and nonlocal conditions, Abstr. Appl. Anal., 2011 (2011), 120.
27. F. Li, J. Liang, H. K. Xu, Existence of mild solutions for fractional integrodifferential equation of Sobolev type with nonlocal conditions, J. Math. Anal. Appl., 391 (2012), 510525.
28. N. Ford, M. Morgado, Fractional boundary value problems: Analysis and numerical methods, Fract. Calc. Appl. Anal., 14 (2011), 554567.
29. C. Goodrich, Existence and uniqueness of solutions to a fractional differencial equation with nonlocal conditions, Comput. Math. Appl., 61 (2011), 191202.
30. D. Guo, V. Lakshmikantham, X. Liu, Nonlinear integral equations in abstract spaces, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
31. E. Hesameddini, A. Rahimi, E. Asadollahifard, On the convergence of a new reliable algorithm for solving multiorder fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 34 (2016), 154.
32. M. H. Heydari, M. R. Mahmoudi, A. Shakiba, et al. Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion, Commun Nonlinear Sci., 64 (2018), 98121
33. M. H. Heydari, Z. Avazzadeh, M. R. Mahmoudi, Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variableorder fractional Brownian motion, Chaos, Solitons and Fractals, 124 (2019), 105124
34. F. Jarad, D. Baleanu and A. Abdeljawad, Caputotype modification of the Hadamard fractional derivatives, Adv. Differ. EquNY, 2012 (2012), 142.
35. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, NorthHolland Mathematics Studies, Elsevier, 2006.
36. C. Kou, J. Liu and Y. Ye, Existence and uniqueness of solutions for the Cachytype problems of fractional differential equations, Discrete Dyn. Nat. Soc., 2010 (2010), 115.
37. H. Mönch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Analysis: Theory, Methods & Applications, 4 (1980), 985999.
38. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
39. K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
40. I. Podlubny, I. Petrás, B. M. Vinagre, et al. Analogue realizations of fractionalorder controllers, Nonlinear Dynam., 29 (2002), 281296.
41. R. Roohi, M. H. Heydari, M. Aslami, et al. A comprehensive numerical study of spacetime fractional bioheat equation using fractionalorder Legendre functions, The European Physical Journal Plus, 133 (2018), 412.
42. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
43. D. Sierociuk, A. Dzielinski, G. Sarwas, I. Petras, I. Podlubny, T. Skovranek, Modelling heat transfer in heterogeneous media using fractional calculus, Philos. T. R. Soc. A, 371 (2013), 20120146.
44. S. Szufla, On the application of measure of noncompactness to existence theorems, Rendiconti del Seminario Matematico della Universita di Padova, 75 (1986), 114.
45. Y. Y. Gambo, F. Jarad, D. Baleanu, et al. On Caputo modification of the Hadamard fractional derivatives, Adv. Differ. EquNY, 2014 (2014), 10.
46. A. Yacine and B. Nouredine, boundary value problem for CaputoHadamard fractional differential equations, Surveys in Mathematics and its Applications, 12 (2017), 103115.
47. H. E. Zhang, Nonlocal boundary value problems of fractional order at resonance with integral conditions, Adv. Differ. EquNY, 2017 (2017), 326.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)