Existence and Uniqueness of Solutions for Fractional-Differential Equation with Boundary Condition Using Nonlinear Multi-Fractional Derivatives

4区工程技术 Q1 Mathematics

Mathematical Problems in Engineering Pub Date : 2024-02-12 DOI:10.1155/2024/6844686

Chanon Promsakon, Intesham Ansari, Mecieu Wetsah, Anoop Kumar, Kulandhaivel Karthikeyan, Thanin Sitthiwirattham

引用次数: 0

Abstract

In this article the existence as well as the uniqueness (EU) of the solutions for nonlinear multiorder fractional-differential equations (FDE) with local boundary conditions and fractional derivatives of different orders (Caputo and Riemann–Liouville) are covered. The existence result is derived from Krasnoselskii’s fixed point theorem and its uniqueness is shown using the Banach contraction mapping principle. To illustrate the reliability of the results, two examples are given.

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使用非线性多分式导数的带边界条件的分式微分方程解的存在性和唯一性

本文论述了具有局部边界条件和不同阶分数导数（卡普托和黎曼-黎奥维尔）的非线性多阶分数微分方程（FDE）解的存在性和唯一性（EU）。存在性结果来自 Krasnoselskii 定点定理，其唯一性则通过巴拿赫收缩映射原理得到证明。为了说明结果的可靠性，我们举了两个例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Problems in Engineering 工程技术-工程：综合

CiteScore

4.00

自引率

0.00%

发文量

2853

审稿时长

4.2 months

期刊介绍： Mathematical Problems in Engineering is a broad-based journal which publishes articles of interest in all engineering disciplines. Mathematical Problems in Engineering publishes results of rigorous engineering research carried out using mathematical tools. Contributions containing formulations or results related to applications are also encouraged. The primary aim of Mathematical Problems in Engineering is rapid publication and dissemination of important mathematical work which has relevance to engineering. All areas of engineering are within the scope of the journal. In particular, aerospace engineering, bioengineering, chemical engineering, computer engineering, electrical engineering, industrial engineering and manufacturing systems, and mechanical engineering are of interest. Mathematical work of interest includes, but is not limited to, ordinary and partial differential equations, stochastic processes, calculus of variations, and nonlinear analysis.