ON THE ULAM-HYERS-RASSIAS STABILITY FOR A BOUNDARY VALUE PROBLEM OF IMPLICIT ψ-CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION

ON THE ULAM-HYERS-RASSIAS STABILITY FOR A BOUNDARY VALUE PROBLEM OF IMPLICIT ψ-CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATION

Y. AWAD, I. KADDOURA

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Abstract. The main purpose of this paper is to study the existence and uniqueness of a nonlinear implicit ψ-Caputo fractional order integro-differential boundary value problem using Schauder's and Banach's fixed point theorems. Besides, we study its stability using Ulam-Hyers-Rassias stability type. Finally, we demonstrate our main findings, with a particular case example included to show the significance of our results.

Implicit fractional-orders differential equation, ψ-Caputo derivative, existence results, boundary value problems, Green's function, Ulam stability.

AMS Subject Classification: Primary 26A33; Secondary 34K45, 47G10.