Mixed Problem for Partial Differential Equation of Large Time Variable Order

Abstract

An algorithm for solving a class of linear variable order fractional partial differential equations (FPDEs) is presented in this paper. We utilized a combination of Caputo fractional derivatives with the Haar wavelet collocation method (HWCM) and Eiler–Fouirier method to solve linear variable order FPDEs. Fractional calculus is a more complex form of standard mathematical calculus. FPDEs is an equation that uses a fractional derivative (FD) by t > 0 (time variable) and two derivatives by x ∈ R (speciousness variable). FPDEs are used to model a wide range of phenomena in the fields of science, electric circuits, engineering and mechanical systems. In this paper we study solvability of the Cauchy and boundary value problem is constructed for FPDE. Parabolic pseudodifferential equations this pseudodifferential operator with noon-smooth symbols introduced by Eidel’man S. and Drin’ Ya. for the first time. The Haar wavelets, which are made up of piecewise constant functions, are the mathematically simplest of all the wavelet families. These wavelets have the advantage of being analytically integrated any number of times. In Haar wavelet two functions, sclaling and mother function, play an essential role. We may therefore draw the conclusion that the Haar wavelet collocation method and Eiler–Fouirier method is an effective method for finding the solution of linear VO FPDEs.