SOME RESULTS OF THE NONLINEAR HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH ALGEBRA

SOME RESULTS OF THE NONLINEAR HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH ALGEBRA

Y. Awad

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Abstract

In this paper, a fixed point theorem of Dhage is used to prove under mixed Lipschitz and Caratheodory conditions the existence of solutions for a nonlinear hybrid fractional differential equation in Banach algebra with two-point integral hybrid boundary conditions. Furthermore, sufficient conditions for existence and uniqueness of mild solutions are derived. In addition, the Ulam-Hyers types of stability of solutions are established. Finally, a numerical example is given to clarify the acquired outcomes.

Keywords

Dhage fixed point theorem, Hybrid fractional integro-differential equations, Existence results, Banach Algebra, Boundary value problems, Green’s function, Hyers-Ulam stability.