Converting fractional differential equations into partial differential equations

He, Ji‐Huan; Li, Zheng-Biao

doi:10.2298/tsci110503068h

Cited by 111 publications

(68 citation statements)

References 6 publications

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“…Since most fractional differential equations do not have exact analytic solutions, approximation and numerical techniques, therefore, are used extensively. Recently, He and Lee [5,6,7] suggested a fractional complex trans-form instrument that converts fractional derivatives into classical derivatives. They considered the following PDE:…”

Section: Introduction and Discussionmentioning

confidence: 99%

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

Katatbeh¹,

Abu-Irwaq²,

Alquran³

et al. 2014

Int. J. of Pure and Appl. Math.

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Section: Introduction and Discussionmentioning

confidence: 99%

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

Katatbeh¹,

Abu-Irwaq²,

Alquran³

et al. 2014

Int. J. of Pure and Appl. Math.

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“…Some significant properties of the modified Riemann-Liouville derivative can be summarized as follows [23,24]:…”

Section: Modified Riemann-liouville Derivative and Some Of Its Propermentioning

confidence: 99%

The modified simple equation method for solving some fractional-order nonlinear equations

Kaplan

Bekir

2016

Pramana - J Phys

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Nonlinear fractional differential equations are encountered in various fields of mathematics, physics, chemistry, biology, engineering and in numerous other applications. Exact solutions of these equations play a crucial role in the proper understanding of the qualitative features of many phenomena and processes in various areas of natural science. Thus, many effective and powerful methods have been established and improved. In this study, we establish exact solutions of the time fractional biological population model equation and nonlinear fractional Klein-Gordon equation by using the modified simple equation method.

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“…Subsequently, f ( t ) and g ( t ) satisfy the definition of the modified Riemann–Liouville derivative and h ( t ) is an α order differentiable function. Some useful formulas and results of the fractional modified Riemann–Liouville derivative are summarized in References .

D_{t}^{α} x^{β} = \frac{normalΓ (1 + β)}{normalΓ (1 + β - α)} x^{β - α}, β > 0

D_{t}^{α} (f (t) g (t)) = g (t) D_{t}^{α} f (t) + f (t) D_{t}^{α} g (t)

D_{t}^{α} h [f (t)] = h_{f}^{'} [f (t)] D_{t}^{α} f (t) = D_{f}^{α} h [f (t)] {(f^{'} (t))}^{α}

The aforementioned equations are hired in fractional calculus in the following sections.…”

Section: Brief Of Modified Riemann–liouville Derivativementioning

confidence: 99%

Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method

Bekir

Aksoy

Çevikel

2014

Math Methods in App Sciences

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In this article, the sub‐equation method is presented for finding the exact solutions of a nonlinear fractional partial differential equations. For this, the fractional complex transformation method has been used to convert fractional‐order partial differential equation to ordinary differential equation. The fractional derivatives are described in Jumarie's the modified Riemann–Liouville sense. We apply to this method for the nonlinear time fractional differential equations. With the aid of symbolic computation, a variety of exact solutions for them are obtained. Copyright © 2014 John Wiley & Sons, Ltd.

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Converting fractional differential equations into partial differential equations

Abstract: A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension

Cited by 111 publications

References 6 publications

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

Solitary Wave Solutions to Time-Fractional Coupled Degenerate Hamiltonian Equations

The modified simple equation method for solving some fractional-order nonlinear equations

Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method

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