Solving space-fractional Cauchy problem by modified finite-difference discretization scheme

This paper deals with the stability convergence analysis for SFCE in the sense of Riemann-Liouville derivative. A modified FDDS is developed utilizing the fractionally-shifted Grünwald formula in handling the SFCE. In this orientation, a novel operational matrix based on the implicit scheme is proposed for solving such issue. The stability features of steady states of the SFCE are investigated numerically. Several numerical applications using the well-known SFCE are tested to demonstrate the capability and feasibility of the method. The acquired results indicate that the proposed method is an appropriate tool for solving various fractional systems arises in physics and engineering.