Analyzing the Existence and Uniqueness of Solutions in Coupled Fractional Differential Equations

被引：0

作者：

Intesham Ansari ^{[1
]}

Rishika Dubey ^{[1
]}

Amita Devi ^{[1
]}

Anoop Kumar ^{[1
]}

机构：

[1] Department of Mathematics and Statistics, School of Basic Sciences, Central University of Punjab, Punjab, Bathinda

来源：

International Journal of Applied and Computational Mathematics | 2025年 / 11卷 / 2期

关键词：

Banach Contraction Mapping principle; Caputo fractional derivative; Coupled fractional differential equation; Krasnoselskii’s fixed point theorem;

D O I：

10.1007/s40819-025-01876-z

中图分类号：

学科分类号：

摘要：

This paper investigates a mixed fractional differential equation (FDE) involving both left-sided and right-sided Caputo fractional derivatives. Our primary contributions are as follows: First, we introduce foundational lemmas and definitions pertinent to the problem. Second, we develop a solution composed of Green’s function and an additional constant term, thoroughly determining the Green’s function and its properties. Third, we establish the existence of solutions using Krasnoselskii’s fixed point theorem and prove their uniqueness through the Banach fixed point theorem. These contributions collectively provide a robust framework for solving mixed FDEs, highlighting the utility of these mathematical methods in addressing complex fractional differential equations. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.

引用

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