Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method

Abstract

One of the prominent nonlinear partial differential equations in mathematical physics is the Clannish Random Walker’s Parabolic (CRWP) equation. This study uses Residual Power Series Method (RPSM) to solve the time fractional CRWP equation. In this equation, the fractional derivatives are considered in Caputo’s sense. The effectiveness of RPSM is illustrated with graphical results. The series solutions are utilized to represent the approximate solutions. Besides, the approximate solutions found by the suggested method ensure good accuracy when compared with the exact solution. Moreover, RPSM efficiently analyzes complex problems that emerge in the related mathematical and scientific fields.

Keywords

• Fractional partial differential equation
• Caputo derivative
• Clannish Random Walker’s Parabolic equation
• residual power series method
• approximate solution

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