Fourth kind Chebyshev Wavelet Method for the solution of multi-term variable order fractional differential equations


Dincel A. T. , TURAL POLAT S. N.

ENGINEERING COMPUTATIONS, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1108/ec-04-2021-0211
  • Title of Journal : ENGINEERING COMPUTATIONS
  • Keywords: Multi-term fractional differential equations, Numerical approximation for FDEs, Fourth kind Chebyshev Wavelets (FKCW), Operational matrix for fractional derivatives, OPERATIONAL MATRIX, NUMERICAL-SOLUTION, INTEGRATION, CALCULUS, OPERATORS

Abstract

Purpose Multi-term variable-order fractional differential equations (VO-FDEs) are powerful tools in accurate modeling of transient-regime real-life problems such as diffusion phenomena and nonlinear viscoelasticity. In this paper the Chebyshev polynomials of the fourth kind is employed to obtain a numerical solution for those multi-term VO-FDEs. Design/methodology/approach To this end, operational matrices for the approximation of the VO-FDEs are obtained using the Fourth kind Chebyshev Wavelets (FKCW). Thus, the VO-FDE is condensed into an algebraic equation system. The solution of the system of those equations yields a coefficient vector, the coefficient vector in turn yields the approximate solution. Findings Several examples that we present at the end of the paper emphasize the efficacy and preciseness of the proposed method. Originality/value The value of the paper stems from the exploitation of FKCWs for the numerical solution of multi-term VO-FDEs. The method produces accurate results even for relatively small collocation points. What is more, FKCW method provides a compact mapping between multi-term VO-FDEs and a system of algebraic equations given in vector-matrix form.