Fuzzy transform algorithm for partial fractional differential equations

Abstract

This paper is devoted for introducing some background theory on the concept of the Fuzzy Transform as new tool for solving fractional order partial differential equations. We then investigate and apply the fuzzy transform on the rate dependent fractional diffusion-wave equation. In the process of this we give a new numerical algorithm, the algorithm will be simulated as a user-subroutine for the mathematical code MATLAB. The time-dependent fractional diffusion equation will be considered to show the efficiency of the algorithm, results will be obtained and compared for different partitions and fractional orders. The approximated results will be compared with the true solution of the differential equation.