A Bernoulli Operational Matrix Method for Solving Nonlinear Multi-Term Fractional Variable-Order Delay Differential Equation

Document Type : Research Article

Authors

1 Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, Iran

2 Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA

3 School of Computing, University of North Florida, Jacksonville, FL 32224, USA

Abstract

This paper investigates the generalized non-linear multi-term delay fractional differential equation of variable order. The Bernoulli operational matrix method is utilized to address a category of these equations, transforming the original problem into a system of algebraic equations amenable to numerical solutions. Sufficient and complete numerical tests are presented to showcase the accuracy, generality, and efficiency of the presented technique, as well as the adaptability of this approach. The numerical results of this method are compared with the exact solution. A comparison of this scheme's results with the exact solution illustrates the method's effectiveness and validity.

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 10, Issue 1
December 2025
Pages 1-16

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History

  • Receive Date: 08 September 2025
  • Revise Date: 15 October 2025
  • Accept Date: 20 October 2025
  • Publish Date: 17 December 2025

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