Existence and Uniqueness of Solution of Fractional Differential Equation Using Non-local Operator
Year: 2024
Type: article
Abstract: Objectives : To investigate the existence and uniqueness of a solution to the non-local Cauchy problem of order using the Atangana Baleanu (AB) fractional derivative operator. Methods : Using Schauder's fixed point theorem and the Arzela-Ascoli theorem, the study proved the existence of a solution to the given problem. Further, it obtains results for the uniqueness of the solution. Findings : This study proves the existence of a solution to the non-local Cauchy problem under the given conditions. Results are also provided for the uniqueness of the solution. Novelty : A novel approach to fractional differential equations is represented by applying Atangana-Baleanu fractional derivative operator to the non-local Cauchy problem. Schauder's fixed point theorem and Arzela-Ascoli's theorem, are used to show existence and uniqueness. Further, one detailed example has been solved. Keywords: Existence, Uniqueness, Non-local operator, Schauder fixed point theorem, Arzela-Ascoli theorem, Cauchy problem
Authors: Amjad S Shaikh, Munzarin A Sajjan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403223040