Abstract
The aim of this paper is to give the existence as well as the uniqueness results for a multipoint nonlocal integral boundary value problem of nonlinear sequential fractional integrodifferential equations. First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Last, but not least, we give two examples to illustrate the results.
Highlights
Fractional differential equations with multipoint boundary conditions have provoked a great deal of attention by many authors; a lot of works have been published on this topic; for more details, we give the following references [16,17,18,19,20,21,22]
In [24], the authors discussed the existence of solutions for fractional differential equations with multipoint boundary conditions
The existence results for sequential fractional integrodifferential equations with nonlocal multipoint and strip conditions were established in [26], and in [27], the authors studied the existence of solutions for nonlinear fractional integrodifferential equations
Summary
In the last few years, fractional differential equations have gained much attention among mathematicians because of the rapid growth and for their applicability in several fields, such as physics, biology, economics, control theory, and engineering; for more details about the theory of fractional differential equations and their applications, we recommend the following articles [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] and the references therein. The existence results for sequential fractional integrodifferential equations with nonlocal multipoint and strip conditions were established in [26], and in [27], the authors studied the existence of solutions for nonlinear fractional integrodifferential equations. Motivated by all these works, and by the fact that there are no papers dealing with nonlinear fractional integrodifferential equations with multipoint and integral boundary value conditions, in this work, we consider the existence and uniqueness of solutions for the following problem:. This paper is organized as follows: in the second section, we give some preliminaries and notations that will be useful throughout the work; after that, in the third section, we establish the main results by using the fixed point theory; and in the last section, we give some examples to illustrate the results
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