A new optimization operational matrix algorithm for solving nonlinear variable-order time fractional convection-diffusion equation

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HASSANI HOSSEIN; Naragirad Eskandar

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2019 | Volume:9 | Issue:1 Page(s): 98-119

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Title

A new optimization operational matrix algorithm for solving nonlinear variable-order time fractional convection-diffusion equation

Author(s)

HASSANI HOSSEIN | Naragirad Eskandar | Issue Writer Certificate

Keywords

Nonlinear variableQ1

order time fractional convectionQ1

diffusion equation Operational matrices Optimization algorithm Generalized polynomials (GPs) Control parametersQ1

Abstract

In this paper, a new and effective optimization algorithm is proposed for solving the nonlinear time fractional convection-diffusion equation with the concept of variable-order fractional derivative in the Caputo sense. For finding the solution, we first introduce the generalized polynomials (GPs) and construct the variable-order operational matrices. In the proposed optimization technique, the solution of the problem under consideration is expanded in terms of GPs with unknown free coefficients and control parameters. The main advantage of the presented method is to convert the variable-order fractional partial differential equation to a system of nonlinear algebraic equations. Also, we obtain the free coefficients and control parameters optimally by minimizing the error of the approximate solution. Finally, the numerical examples confirm the high accuracy and efficiency of the proposed method in solving the problem under study.

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APA: Copy

HASSANI, HOSSEIN, & Naragirad, Eskandar. (2019). A new optimization operational matrix algorithm for solving nonlinear variable-order time fractional convection-diffusion equation. ADVANCES IN MATHEMATICAL MODELING, 9(1 ), 98-119. SID. https://sid.ir/paper/243905/en

Vancouver: Copy

HASSANI HOSSEIN, Naragirad Eskandar. A new optimization operational matrix algorithm for solving nonlinear variable-order time fractional convection-diffusion equation. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2019;9(1 ):98-119. Available from: https://sid.ir/paper/243905/en

IEEE: Copy

HOSSEIN HASSANI, and Eskandar Naragirad, “A new optimization operational matrix algorithm for solving nonlinear variable-order time fractional convection-diffusion equation,” ADVANCES IN MATHEMATICAL MODELING, vol. 9, no. 1 , pp. 98–119, 2019, [Online]. Available: https://sid.ir/paper/243905/en

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