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.

Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation

“…Stochastic fractional differential equations (SFDEs) are a powerful mathematical framework with numerous applications in science and engineering [1][2][3]. They combine stochastic processes, which address unpredictability, with fractional calculus, which includes memory and non-local effects, allowing them to simulate complicated events that classical differential equations cannot.…”

Orthonormal Bernoulli Polynomials for Solving a Class of Two Dimensional Stochastic Volterra–Fredholm Integral Equations

“…Stochastic processes occur in many real issues such as control systems [5], biological population growth [6], biology and medicine [7]. In recent decades, due to the importance of stochastic differential equations (SDE) and stochastic integral equations (SIE) in modeling programs where there is considerable uncertainty, scientists have studied the stochastic process and its applications [8][9][10][11][12].…”

On dual Bernstein polynomials and stochastic fractional integro‐differential equations

“…Recently, research efforts were devoted to random analysis in the fields of biology, mathematics, fluid mechanics, chemistry, and physics with this class of equations. 6,7 Bearing these ideas in mind, this paper addresses the numerical solution of the SFIDE.…”

“…Because random or stochastic functional equations occur in many problems, such as the growth of biological populations, 3 reactor dynamics, 4 and control systems, 5 finding their solution is of key importance. Recently, research efforts were devoted to random analysis in the fields of biology, mathematics, fluid mechanics, chemistry, and physics with this class of equations 6,7 . Bearing these ideas in mind, this paper addresses the numerical solution of the SFIDE.…”