Efficient Galerkin solution of stochastic fractional differential equations using second kind Chebyshev wavelets

Abstract

‎Stochastic fractional differential equations (SFDEs) have been used for modeling many physical problems in the fields of turbulance‎, ‎heterogeneous‎, ‎flows and matrials‎, ‎viscoelasticity and electromagnetic theory‎. ‎In this paper‎, ‎an‎ efficient wavelet Galerkin method based on the second kind Chebyshev wavelets are proposed for approximate solution of SFDEs‎. ‎In ‎this ‎app‎roach‎‎, ‎o‎perational matrices of the second kind Chebyshev wavelets ‎are used ‎for reducing SFDEs to a linear system of algebraic equations that can be solved easily‎. ‎C‎onvergence and error analysis of the proposed method is ‎considered‎.‎ ‎Some numerical examples are performed to confirm the applicability and efficiency of the proposed method‎.

Keywords

• Fractional ‎calculus
• ‎ ‎Stochastic ‎calculus
• ‎ ‎Stochastic fractional differential ‎equations
• ‎ ‎Second kind Chebyshev ‎wavelets
• ‎ ‎Operational ‎matrix
• ‎ ‎Wavelet Galerkin method