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

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. Fo...

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Bibliographic Details
Published inAxioms Vol. 13; no. 9; p. 627
Main Authors Mahmudov, Nazim I., Cival Buranay, Suzan, Chin, Mtema James
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2024
Subjects
algorithm
Algorithms
Approximation
Book publishing
Cauchy problems
Cauchy–Euler equation
collocation method
Computing time
convergence analysis
Euler-Lagrange equation
existence and uniqueness
Integral transforms
Mathematical analysis
Methods
Numerical analysis
Numerical methods
Ordinary differential equations
Simulation methods
Uniqueness
United States
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13090627