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 Solving Time-Space Fractional Cauchy Problem with Constant Coecients by Finite Dierence Method

Reem Edwan, Rania Saadeh, , Mohammed Al-Smadi,
Published in Springer, Singapore
2020
Pages: 25 - 46
Abstract

In this chapter, we present the time-space-fractional Cauchy equation with constant coefficients, the space and time-fractional derivative are described in the Riemann-Liouville sense and Caputo sense, respectively. The implicit scheme is introduced to solve time-space-fractional Cauchy problem in a matrix form by utilising fractionally Grünwald formulas for discretization of Riemann-Liouville fractional integral, and L1-algorithm for the discretization of time-Caputo fractional derivative, additionally, we provided a proof of the von Neuman type stability analysis for the fractional Cauchy equation of fractional order. Several numerical examples are introduced to illustrate the behaviour of approximate solution for various values of fractional order.

About the journal
JournalData powered by TypesetCommunications in Mathematical Computations and Applications
PublisherData powered by TypesetSpringer, Singapore
ISSN23646748
Open AccessNo