Two Linearized Schemes for One-Dimensional Time and Space Fractional Differential Equations

Victor N. Orlov (), Asmaa M. Elsayed and Elsayed I. Mahmoud
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Victor N. Orlov: Department of Applied Mathematics, Moscow State University of Civil Engineering, Yaroslavskoe Shosse 26, 129337 Moscow, Russia
Asmaa M. Elsayed: Department of Applied Mathematics, Moscow State University of Civil Engineering, Yaroslavskoe Shosse 26, 129337 Moscow, Russia
Elsayed I. Mahmoud: Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Mathematics, 2022, vol. 10, issue 19, 1-16

Abstract: This paper investigates the solution to one-dimensional fractional differential equations with two types of fractional derivative operators of orders in the range of ( 1 , 2 ) . Two linearized schemes of the numerical method are constructed. The considered FDEs are equivalently transformed by the Riemann–Liouville integral into their integro-partial differential problems to reduce the requirement for smoothness in time. The analysis of stability and convergence is rigorously discussed. Finally, numerical experiments are described, which confirm the obtained theoretical analysis.

Keywords: time and space fractional differential equations; linearized schemes; integro-differential equation; stability; convergence; weighted and shifted Grünwald difference operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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