An efficient computational approach for nonlinear variable order fuzzy fractional partial differential equations

Abstract

This research work employs the Bernstein spectral technique based on Bernstein polynomials to analyze and to obtain the approximate numerical solution of a class of variable order fuzzy partial differential equations (PDEs) and its some particular cases using the basic properties of fuzzy theory. We analyze a variable order mathematical fuzzy model where the coefficients, unknown functions, initial and boundary conditions are some fuzzy numbers and fuzzy valued functions. The variable order fuzzy operational matrix of Bernstein polynomials is derived for fuzzy fractional derivatives with respect to space and time where the fuzzy derivative is taken in Caputo sense. The Bernstein fuzzy operational matrix is applied to concerned non-linear fuzzy space-time fractional variable order reaction–diffusion equations which reduce into a system of non-linear fuzzy algebraic equations and can be deal with using the method given in the literature. To validate the high efficiency and capability of the proposed numerical scheme few test examples are reported with computation of the absolute error for the obtained numerical solution. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.