Series splutions for initial-value problems of time fractional generalized anomalous diffusion equations

Abstract

In this paper, we formulate an initial-value problem of generalized anomalous diffusion equation consisting second order in two dimensional space and fractional order in time derivatives and then solve it by applying a series involving bilinear Eigen functions. Also, we evaluate a numerical approximation formula of this solution and also discuss its some special cases.

Keywords

• Initial value problem
• Generalized anomalous diffusion equation
• Riemann-Liouville fractional order derivative
• Caputo derivative
• Bilinear Eigen functions
• Numerical approximation formula