An approximate method based on Bernstein polynomials for solving fractional PDEs with proportional delays

Iranian Journal of Numerical Analysis and Optimization

مقاله 11، دوره 10، شماره 2 - شماره پیاپی 18، 2020، صفحه 223-239   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v10i2.86274

نویسندگان

A. Ketabdari؛ M.H. Farahi^* ؛ S. Effati

Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

چکیده

We apply a new method to solve fractional partial differential equations (FPDEs) with proportional delays. The method is based on expanding the unknown solution of FPDEs with proportional delays by the basis of Bernstein polynomials with unknown control points and uses operational matrices with the least-squares method to convert the FPDEs with proportional de lays to an algebraic system in terms of Bernstein coefficients (control points) approximating the solution of FPDEs. We use the Caputo derivatives of de gree 0 < α ≤ 1 as the fractional derivatives in our work. The main advantage of using this technique is that the method can easily be employed to a variety of FPDEs with or without proportional delays, and also the method offers a very simple and flexible framework for direct approximating of the solution of FPDEs with proportional delays. The convergence analysis of the present method is discussed. We show the effectiveness and superiority of the method by comparing the results obtained by our method with the results of some available methods in two numerical examples.

کلیدواژه‌ها

Fractional partial differential equation؛ Bernstein polynomial؛ Operational matrix؛ Caputo derivative

مراجع