Open Access

ARTICLE

A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

by Sergiy Reutskiy¹, Yuhui Zhang^2,*, Jun Lu^3,*, Ciren Pubu⁴

1 A. Pidhornyi Institute of Mechanical Engineering Problems of NAS of Ukraine, Kharkiv, 61046, Ukraine
2 College of Mechanics and Materials, Hohai University, Nanjing, 211100, China
3 Nanjing Hydraulic Research Institute, Nanjing, 210029, China
4 Shigatse Everest Urban Investment and Development Group Co, Ltd., 857000, China

* Corresponding Authors: Yuhui Zhang. Email: ; Jun Lu. Email:

(This article belongs to the Special Issue: New Trends on Meshless Method and Numerical Analysis)

Computer Modeling in Engineering & Sciences 2024, 139(2), 1583-1612. https://doi.org/10.32604/cmes.2023.044878

Received 10 August 2023; Accepted 17 November 2023; Issue published 29 January 2024

Abstract

This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations (FODEs) which have been widely used in modeling various phenomena in engineering and science. An approximate solution of the system is sought in the form of the finite series over the Müntz polynomials. By using the collocation procedure in the time interval, one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure. This technique also serves as the basis for solving the time-fractional partial differential equations (PDEs). The modified radial basis functions are used for spatial approximation of the solution. The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above. Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.

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Keywords

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