Work

On the Existence, Uniqueness and a Numerical Approach to the Solution of Fractional Cauchy–Euler Equation

Year: 2024

Type: article

Abstract: In this research paper, we consider a model of the fractional Cauchy–Euler-type equation, where the fractional derivative operator is the Caputo with order 0<α<2. The problem also constitutes a class of examples of the Cauchy problem of the Bagley–Torvik equation with variable coefficients. For proving the existence and uniqueness of the solution of the given problem, the contraction mapping principle is utilized. Furthermore, a numerical method and an algorithm are developed for obtaining the approximate solution. Also, convergence analyses are studied, and simulations on some test problems are given. It is shown that the proposed method and the algorithm are easy to implement on a computer and efficient in computational time and storage.

Source: Axioms

DOI: 10.3390/axioms13090627

Authors: Nazim I. Mahmudov, Suzan Cival Buranay, Mtema James Chin

Institutions: Eastern Mediterranean University, Azerbaijan State University of Economics

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

OpenAlex ID: W4402525264

FWCI: 0.69

Cites: 29

Cited by: 2

Related to: 10