Numerical study of multi-order fractional differential equations with constant and variable coefficients

Journal of Taibah University for Science

Muhammad Bilal Riaz¹  Abdon Atangana¹  Ali Raza²  Imran Talib² 

[1] Institute for Groundwater Studies, University of the Free State, Bloemfontein, South Africa;Nonlinear Analysis Group (NAG), Mathematics Department, Virtual University of Pakistan, Lahore, Pakistan;

关键词: Multi-order fractional differential equations;    operational matrices;    shifted Legendre polynomials;    Caputo derivative;    Paraskevopoulos's method;    65M99;   

DOI  :  10.1080/16583655.2022.2089831

来源: DOAJ

【 摘 要 】

In this manuscript, a numerical method based on the conjunction of Paraskevopoulos's algorithm and operational matrices is developed to solve numerically the multi-order linear and nonlinear fractional differential equations. By means of this conjunction, the multi-order problem is decomposed into a system of differential equations of fractional order which are then solved by employing operational matrices approach. The accuracy and efficiency of the method is examined by taking some examples. In addition, the numerical results presented in Pak et al. [Analytical solutions of linear inhomogeneous fractional differential equation with continuous variable coefficients. Adv Differ Equ. 2019;2019(256):1–22] are improved in our work.

【 授权许可】

Unknown