Study of integral type implicit multi term fractional delay differential equation with multi strip conditions

Abstract

This paper is concerned with the existence and functional stability of solutions to some class of integral-type implicit fractional-order differential equations using multi-strip subsidiary conditions. Contrary to the single-term fractional-order differential operators, in the present study, multi-term operators are involved, and the effect of the past time by a proportional delay is taken into consideration. The problem under investigation is converted into a fixed-point problem. The results are based on Krasnoselskii’s fixed-point theorem, which establishes the existence of the solution, and Banach’s, which establishes its uniqueness. The Ulam-Hyers type stability analysis is used in the study of the behavior of the solutions under perturbations. An example is given at the end to confirm the reliability of the results obtained.