Analytical solutions of multi-term time fractional differential equations and application to unsteady flows of generalized viscoelastic fluid

Ming, Chunying; Liu, Fawang; Zheng, Liancun; Turner, Ian; Anh, Vo

doi:10.1016/j.camwa.2016.08.012

Cited by 51 publications

(18 citation statements)

References 41 publications

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“…Fractional arithmetic and fractional differential equations appeared in many disciplines, including medicine [1], economics [2], dynamical problems [3,4], chemistry [5], mathematical physics [6], traffic model [7], fluid flow [8], and so on.…”

Section: Introductionmentioning

confidence: 99%

An optimal method for approximating the delay differential equations of noninteger order

2018

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The main purpose of this paper is to use a method with a free parameter, named the optimal asymptotic homotopy method (OHAM), in order to obtain the solution of delay differential equations, delay partial differential equations, and a system of coupled delay equations featuring fractional derivative. This method is preferable to others since it has faster convergence toward homotopy perturbation method, and the convergence rate can be set as a controlled area. Various examples are given to better understand the use of this method. The approximate solutions are compared with exact solutions as well. MSC: 35R11; 65F10; 26A33

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Section: Introductionmentioning

confidence: 99%

An optimal method for approximating the delay differential equations of noninteger order

2018

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“…Fractional arithmetic and fractional differential equations appeared in many sciences, including medicine [11], economics [21], dynamical problems [5,15], chemistry [17,19], mathematical physics [7], traffic model [16] and fluid flow [12] and so on.…”

Section: Introductionmentioning

confidence: 99%

A reliable mixed method for singular integro-differential equations of non-integer order

Băleanu

Darzi

Agheli

2018

Math. Model. Nat. Phenom.

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It is our goal in this article to apply a method which is based on the assumption that combines two methods of conjugating collocation and multiple shooting method. The proposed method can be used to find the numerical solution of singular fractional integro-differential boundary value problems (SFIBVPs) Dϑ y(t) + η ∫0t (t−s)ς−1 y(s) ds = g(t), 1 < ϑ ≤ 2, 0 < ς< 1, η ∈ ℝ, where Dϑ denotes the Caputo derivative of order ϑ. Meanwhile, in a separate section the existence and uniqueness of this method is also discussed. Two examples are presented to illustrate the application and further understanding of the methods.

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“…Time-fractional diffusion equations, as a kind of anomalous diffusion equations, are used to describe the behaviour of different real-life transport processes with long memory, where the diffusion rate is not consistent with the classical Brownian motion model [26] (e.g. the behaviour of flow through porous media [27] and relaxation phenomena in viscoelastic materials [28]. For more information on time-fractional anomalous diffusion systems, the readers are referred to [29,30] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Robust control for time‐fractional diffusion processes: application in temperature control of an alpha silicon carbide cutting tool

Sayyaf

Tavazoei

2018

IET Control Theory & Applications

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Analytical solutions of multi-term time fractional differential equations and application to unsteady flows of generalized viscoelastic fluid

Cited by 51 publications

References 41 publications

An optimal method for approximating the delay differential equations of noninteger order

An optimal method for approximating the delay differential equations of noninteger order

A reliable mixed method for singular integro-differential equations of non-integer order

Robust control for time‐fractional diffusion processes: application in temperature control of an alpha silicon carbide cutting tool

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