Existence Results for Impulsive Fractional Integrodifferential Equations Involving Integral Boundary Conditions

Abstract

This research paper is devoted to investigating the existence results for impulsive fractional integrodifferential equations in the form of Atangana - Baleanu - Caputo (ABC) fractional derivative, by using Gronwall–Bellman inequality and Krasnoselskii’s fixed point theorem to study the existence and uniqueness of the problem with integral boundary conditions. At the end, the examples are illustrated to verify results.

On Implicit Atangana–Baleanu–Caputo Fractional Integro-Differential Equations with Delay and Impulses

“…Researchers have employed fxed point theory and nonlinear analysis techniques to fnd the results of investigations. Te authors have investigated the theory of these diferential equations, see reference [18][19][20][21][22]. However, the study of impulsive problems using the theory of fractional calculus has also progressed well.…”

Analysis of Existence and Stability Results for Impulsive Fractional Integro-Differential Equations Involving the Atangana–Baleanu–Caputo Derivative under Integral Boundary Conditions

“…In addition, BVPs with integral boundary conditions have numerous contributions of mathematical modeling to the heat conduction process, hemic conduction process, and hydrodynamics issues. Many authors have investigated FDEs with boundary conditions [14][15][16][17][18][19][20][21][22][23].…”