Existence of Solutions for Nonlocal Boundary Value Problem of Hadamard Fractional Differential Equations

Abstract

We investigate the existence and uniqueness of solutions for Hadamard fractional differential equations with nonlocal integral boundary conditions, by using the Leray-Schauder nonlinear alternative, Leray Schauder degree theorem, Krasnoselskiis fixed point theorem, Schaefers fixed point theorem, Banach fixed point theorem, Nonlinear Contractions. Two examples are also presented to illustrate our results.

Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems

“…It is well known that fractional order dierential equations provide an excellent setting for capturing, in a model framework, real-world problems in many disciplines, such as chemistry, physics, engineering, biology and ecology [29,41,35,50,30,24,27,25] . In recent years, there has been a signicant development in ordinary and partial dierential equations involving fractional derivatives, see the monographs of Podlubny [41], Kilbas et al [29], Zhou et al [50], and the recent papers [49,30,4,27,28,23,26,8,21,38] and the references therein.…”

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“…[16,30], to see interesting results in the theory of fractional calculus and fractional differential equations, the reader may consult the monographs by; Abbas et al [8,9], Kilbas et al [22], Oldham et al [26], Podlubny [27], Samko et al [28], Zhou et al [33], and the papers by Abbas et al [3,5], Benchohra et al [12], Lakshmikantham et al [23,24,25]. Other recent results are provided in [11,13,17,18,19,20,21,29,31,32]. Attractivity results for various classes of fractional differential equations are considered in [1,2,4,6,10].…”

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