Solving Nonlinear Variable-Order Time Fractional Convection-Diffusion Equation with Generalized Polynomials

H. Hassani*, J. A. Tenreiro Machado, Z. Avazzadeh, E. Naraghirad

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingChapterpeer-review

Abstract

This chapter presents a new nonlinear variable-order (VO) time fractional convection-diffusion equation (NV-TFCDE). The model generalizes the standard fixed-order nonlinear time fractional convection-diffusion equation. The VO time fractional derivative is described in the Caputo type leading to an optimization method for the NV-TFCDE. The proposed approach is based on a new class of basis functions, namely the generalized polynomials (GP). The solution of the problem under consideration is expanded in terms of the GP with unknown free coefficients (FC) and control parameters (CP). A new VO time fractional operational matrix (V-TFOM) for the GP transforms the problem into a system of nonlinear algebraic equations with unknown FC and CP leading to the approximate solution. Several numerical examples show that the proposed method is efficient.

Original languageEnglish
Title of host publicationNonlinear Physical Science
PublisherSpringer Science and Business Media Deutschland GmbH
Pages147-161
Number of pages15
DOIs
Publication statusPublished - 2022

Publication series

NameNonlinear Physical Science
ISSN (Print)1867-8440
ISSN (Electronic)1867-8459

Keywords

  • Control parameters
  • Free coefficients
  • Generalized polynomials
  • Optimization method
  • Variable-order time fractional convection-diffusion equation
  • Variable-order time fractional operational matrix

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