Solving Time-Space-Fractional Cauchy Problem with Constant Coefficients by Finite-Difference Method

Reem Edwan; Rania Saadeh; Samir Hadid; Mohammed Al-Smadi; Shaher Momani

doi:10.1007/978-981-15-8498-5_2

Solving Time-Space-Fractional Cauchy Problem with Constant Coefficients by Finite-Difference Method

Reem Edwan
, Rania Saadeh
, Samir Hadid
, Mohammed Al-Smadi
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

Taibah University
Zarqa University
Ajman University
Al-Balqa Applied University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

26 Scopus citations

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.

Original language	English
Title of host publication	Forum for Interdisciplinary Mathematics
Publisher	Springer
Pages	25-46
Number of pages	22
DOIs	https://doi.org/10.1007/978-981-15-8498-5_2
State	Published - 2020

Publication series

Name	Forum for Interdisciplinary Mathematics
ISSN (Print)	2364-6748
ISSN (Electronic)	2364-6756

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10.1007/978-981-15-8498-5_2

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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 Gr{\"u}nwald 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.",

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AU - Saadeh, Rania

AU - Hadid, Samir

AU - Al-Smadi, Mohammed

AU - Momani, Shaher

PY - 2020

Y1 - 2020

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AB - 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.

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PB - Springer

ER -

Solving Time-Space-Fractional Cauchy Problem with Constant Coefficients by Finite-Difference Method

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