Abstract
In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.
Highlights
Differential equations of fractional order have been proved to be valuable tools in the modeling of many phenomena of various fields of science and engineering
We study existence and uniqueness of the problem for the system of nonlinear fractional differential equations of form cD0α x t f t, x t, t ∈ 0, T, 1.1 with the nonlocal and integral boundary condition
Assume that x t is a solution of nonlocal boundary value problem 3.1 and 3.2, using Lemma 2.6, we get x t I0α y t c1, c1 ∈ Rn
Summary
Differential equations of fractional order have been proved to be valuable tools in the modeling of many phenomena of various fields of science and engineering. There are several approaches to fractional derivatives such as Riemann-Liouville, Caputo, Weyl, Hadamar and Grunwald-Letnikov, and so forth. Applied problems require those definitions of a fractional derivative that allow the utilization of physically interpretable. The study of existence and uniqueness, periodicity, asymptotic behavior, stability, and methods of analytic and numerical solutions of fractional differential equations have been studied extensively in a large cycle works see, e.g., 10, 18–37 and the references therein. We study existence and uniqueness of the problem for the system of nonlinear fractional differential equations of form cD0α x t f t, x t , t ∈ 0, T , 1.1 with the nonlocal and integral boundary condition.
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