On FBDF5 Method for Delay Differential Equations of Fractional Order with Periodic and Anti-Periodic Conditions

Heris, Mahdi Saedshoar; Javidi, Mohammad

doi:10.1007/s00009-017-0932-8

Cited by 16 publications

(3 citation statements)

References 15 publications

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“…Some numerical methods for FDDEs are introduced in [20][21][22][23] and etc. Heris and Javidi [24] proposed a numerical method based on fractional backward differential formulas (FBDF) for solving fractional delay differential equations. Also they found the Green's functions for this equation corresponding to periodic/anti-periodic conditions in terms of the functions of Mittag Leffler type.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of a fractional differential equation in the theory of viscoelastic fluids

Saghali¹,

Saei²,

Javidi³

et al. 2021

Bul. Kar. Univ. - Math.

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The aim of this paper is to present analytical solutions of fractional delay differential equations (FDDEs) of an incompressible generalized Oldroyd-B fluid with fractional derivatives of Caputo type. Using a modification of the method of separation of variables the main equation with non-homogeneous boundary conditions is transformed into an equation with homogeneous boundary conditions, and the resulting solutions are then expressed in terms of Green functions via Laplace transforms. This results presented in two condition, in first step when 0 ≤ α, β ≤ 1/2 and in the second step we considered 1/2 ≤ α, β ≤ 1, for each step 1,2 for the unsteady flows of a generalized Oldroyd-B fluid, including a flow with a moving plate, are considered via examples.

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Section: Introductionmentioning

confidence: 99%

Analytical solution of a fractional differential equation in the theory of viscoelastic fluids

Saghali¹,

Saei²,

Javidi³

et al. 2021

Bul. Kar. Univ. - Math.

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“…In fact, the evolution of a delay differential system is more complex than the classical one as it relies on its current time as well on its past stages. For some recent works on fractional differential equations with delay, we refer the reader to a series of articles and the references cited therein. It is worth mentioning that partial differential equations with delay have useful applications in biology, control systems, medicine, population ecology, and so on .…”

Section: Introductionmentioning

confidence: 99%

Stability and convergence of difference methods for two‐dimensional Riesz space fractional advection‐dispersion equations with delay

Heris

Javidi

Ahmad

2020

Comp and Math Methods

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In this article, the Riesz space fractional advection‐dispersion equations with delay in two‐dimensional (RFADED in 2D) are considered. The Riesz space fractional derivative is approximated with the aid of backward differential formulas method of second order and shifted Grünwald difference operators. We develop the Crank‐Nicolson scheme using the finite difference method for the RFADED in 2D and show that it is conditionally stable and convergent with the accuracy order O(κ2+h2+k2). Finally, some numerical examples are constructed to demonstrate the efficacy and usefulness of the numerical method.

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“…Numerical methods for solving delay fractional differential equations are very important. Recently Saedshoar Heris and Javidi have been introduced fractional backward differential formulas method(FBDF) for solving FDEs with delay ([9]- [10]).…”

Section: Introductionmentioning

confidence: 99%

Second order difference approximation for a class of Riesz space fractional advection-dispersion equations with delay

Heris,

Javidi

2018

Preprint

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In this work, we propose numerical scheme for the Riesz space fractional advectiondispersion equations with delay (RFADED). Firstly, we find the analytical solution for RFADED in terms of the functions of Mittag-Leffler type. Secondly, we introduce fractional backward differential formulas (FBDF) method and shifted Grünwald method. Stability and convergency of these methods have been proved. Thirdly, Crank-Nicolson scheme for solving this problem is proposed. We prove that the scheme is conditionally stable and convergent with the order accuracy of O(κ 2 + h 2 ). Finally, some numerical examples are given to show the effectiveness of the numerical method and the results are in excellent agreement with the theoretical analysis.

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On FBDF5 Method for Delay Differential Equations of Fractional Order with Periodic and Anti-Periodic Conditions

Cited by 16 publications

References 15 publications

Analytical solution of a fractional differential equation in the theory of viscoelastic fluids

Analytical solution of a fractional differential equation in the theory of viscoelastic fluids

Stability and convergence of difference methods for two‐dimensional Riesz space fractional advection‐dispersion equations with delay

Second order difference approximation for a class of Riesz space fractional advection-dispersion equations with delay

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