ANALYSIS OF A CLASS OF FRACTIONAL DELAY INTEGRO-DIFFERENTIAL EQUATIONS WITH RIESZ-CAPUTO DERIVATIVE

Abstract

This paper investigates the existence and uniqueness of solutions for a particular category of fractional delay integro-differential (FDID) equations in the context of Banach space, incorporating the Riesz-Caputo fractional derivative. Employing fractional calculus techniques and multiple fixed-point theorems, we establish a few results regarding both existence and uniqueness. Further, by introducing a partial order in a Banach space of all continuous functions, we look into the existence of extremal solutions. To demonstrate the competence of the suggested outcomes, a few instances are presented at the conclusion. © 2025 American Institute of Mathematical Sciences. All rights reserved.