Existence and Uniqueness of Solutions for the Nonlinear Fractional Differential Equations with Two-point and Integral Boundary Conditions

Yagub Sharifov, S.A. Zamanova, R.A. Sardarova

Abstract

In this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskii’s fixed point theorem.

Keywords

Nonlocal boundary conditions, Caputo fractional derivative, existence, uniqueness, fixed point.

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