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.
Highlights
Fractional integrals and derivatives have been applied for modeling many physical phenomena in fields of nonlinear oscillation of earthquake, fluid-dynamic traffic, continuum and statistical mechanics, signal processing, control theory, and dynamics of interfaces between nanoparticles and subtracts [14,15,16,17,18]
Many phenomena in science that have been modeled by fractional differential equations have some uncertainty, so for deriving a more accurate solution, we need the solution of SFDEs
We review some necessary definitions and mathematical preliminaries about stochastic calculus, fractional calculus and Block Pulse Functions (BPFs) which are required for establishing our results [1,2]
Summary
We review some necessary definitions and mathematical preliminaries about stochastic calculus, fractional calculus and BPFs which are required for establishing our results [1,2]
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