Existence Results for Abc-Fractional Differential Equations With Non-Separated and Integral Type of Boundary Conditions

Abstract

This paper presents a study on the existence theory of fractional differential equations involving Atangana–Baleanu (AB) derivative of order [Formula: see text], with non-separated and integral type boundary conditions. An existence result for the solutions of given AB-fractional differential equation is proved using Krasnoselskii’s fixed point theorem, while the uniqueness of the solution is obtained using Banach contraction principle. Some conditions are proposed under which the given boundary value problem is Hyers–Ulam stable. Examples are given to validate our results.

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“…Atangana and Baleanu [20] provided a new type of fractional algorithm with a stronger approach. Te AB tools provide a modifcation of the CF approach and enable simulations for nonsingular kernels [21][22][23][24]. In diferent fractional studies, the Prabhakar fractional approach is another analytical framework that is not focused in a comprehensive way.…”

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“…Condensed matter computations may easily implement boundary conditions using PBCs. Unified numerical techniques that consider both periodic and periodic systems are possible [9]. In this paper, The ABC-fractional differential equations with periodic boundary conditions that are being considered as follows:…”

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“…Fractional order Differential equations have lately been useful tools for modeling a wide range of phenomena in science and engineering. Control, porous media, electromagnetic, and other domains can benefit from its use [4][5][6]. Depending on the physical situation at hand, this theory employs a variety of boundary conditions.…”

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