Existence and uniqueness of solution for differential equation of fractional order $2<\alpha\leq 3$ with nonlocal multipoint integral boundary conditions

Authors: GHAZALA AKRAM, FAREEHA ANJUM

Abstract: This paper is devoted to the study of nonlinear fractional differential equation involving Caputo fractional derivative of order $2<\alpha\leq3$ with nonlocal multipoint integral boundary conditions. Some efficient results about the existence and uniqueness are obtained by applying the Banach fixed point theorem, Schaefer's fixed point theorem, and a nonlinear alternative for single valued maps. Two examples are given to illustrate the results.

Keywords: Fractional differential equation, Caputo fractional derivative, Riemann--Liouville fractional integral, Banach fixed point theorem, Schaefer's fixed point theorem, nonlinear alternative for single valued maps

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