A NOVEL THIRD KIND CHEBYSHEV WAVELET COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF STOCHASTIC FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

A NOVEL THIRD KIND CHEBYSHEV WAVELET COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF STOCHASTIC FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

S. C. Shiralashetti, L. Lamani

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Abstract

In the formulation of natural processes like emissions, population development,  nancial markets, and the mechanical systems, in which the past a ect both the present and the future, Volterra integro-di erential equations appear. Moreover, as many phenomena in the real world su er from disturbances or random noise, it is normal and healthy for them to go from probabilistic models to stochastic models. This article introduces a new approach to solve stochastic fractional Volterra integro-di erential equations based on the operational matrix method of Chebyshev wavelets of third kind and stochastic operational matrix of Chebyshev wavelets of third kind. Also, we have given the convergence and error analysis of the proposed method. A variety of numerical experiments are carried out to demonstrate our theoretical  ndings.

Keywords

Stochastic Volterra integro-di erential equations, Chebyshev wavelets of third kind, Brownian motion, stochastic operational matrix of Chebyshev wavelets of third kind.