EXISTENCE AND UNIQUENESS RESULTS FOR A TWO-POINT NONLINEAR BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS OF VARIABLE ORDER

EXISTENCE AND UNIQUENESS RESULTS FOR A TWO-POINT NONLINEAR BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS OF VARIABLE ORDER

Y. Awad, Hussein Fakih

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Abstract

In this article, we study the existence and uniqueness of solutions for a two- point boundary value problem of Caputo fractional di erential equation of variable order. The results are obtained by means of Banach's and Krasnoselskii's  xed point theorems. In addition, the obtained results are illustrated with the aid of a numerical example.

Keywords

Caputo derivatives and integrals of variable-order, Boundary value problems, Existence and uniqueness of solutions, Piecewise constant functions, Green's function.