B-spline-based fuzzy transform method for the numerical solution of variable coefficients multi-term fractional differential equations

Articles in Press

Document Type : Research Paper

Authors

1 1. Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran. 2. Department of Applied Mathematics and Informatics, Faculty of Sciences, Kyrgyz-Turkish Manas University, Bishkek, Kyrgyzstan.

2 Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran.

Abstract

In this paper, an effective numerical algorithm based on the
fuzzy transform with cubic B-splines as basic functions is designed
to solve multi-terms fractional differential equations (FDEs, for short) with variable coefficients. An analytical approximation with desirable
regularity is given to the involving initial value problem. The proposed
method provides a non-recursive approximate solution based on an
operational matrix and a vector of known quantities. The convergence
analysis of the method is carried out. An estimation error is also
provided, which enables us to report the error for the problems
whose exact solutions are not available. The good performance of
our method over the available methods is shown by numerical
results.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 20 June 2026

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History

  • Receive Date: 08 December 2025
  • Revise Date: 15 June 2026
  • Accept Date: 20 June 2026

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