Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions

In this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. To this end, we first construct the operator of Riemann–Liouville...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2023; pp. 1 - 13
Main Authors Akhlaghi, S., Tavassoli Kajani, M., Allame, M.
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2023
Hindawi Limited
Subjects
Approximation
Calculus
Collocation methods
Differential equations
Error analysis
Fractional calculus
Laplace transforms
Mathematical analysis
Numerical analysis
Operators (mathematics)
Orthogonal functions
Quadratures
Truncation errors
Upper bounds
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Summary:In this paper, we derive a spectral collocation method for solving fractional-order integro-differential equations by using a kind of Müntz orthogonal functions that are defined on 0,1 and have simple and real roots in this interval. To this end, we first construct the operator of Riemann–Liouville fractional integral corresponding to this kind of Müntz functions. Then, using the Gauss–Legendre quadrature rule and by employing the roots of Müntz functions as the collocation points, we arrive at a system of algebraic equations. By solving this system, an approximate solution for the fractional-order integro-differential equation is obtained. We also construct an upper bound for the truncation error of Müntz orthogonal functions, and we analyze the error of the proposed collocation method. Numerical examples are included to demonstrate the validity and accuracy of the method.
ISSN:2314-4629
2314-4785
DOI:10.1155/2023/6647128