New Fractional Complex Transform for Conformable Fractional Partial Differential Equations

Abstract Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.

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Solution for Non-linear Fractional Partial Differential Equations Using Fractional Complex Transform

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-019-0673-4 ◽

2019 ◽

Vol 5 (3) ◽

Author(s):

T. T. Shone ◽

A. Patra

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Fractional Complex Transform ◽

Non Linear

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New exact solutions of fractional Hirota-Satsuma coupled Korteweg-de Vries equations

Thermal Science ◽

10.2298/tsci1504173c ◽

2015 ◽

Vol 19 (4) ◽

pp. 1173-1176 ◽

Cited By ~ 2

Author(s):

Lian-Xiang Cui ◽

Li-Mei Yan ◽

Yan-Qin Liu

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Exact Solutions ◽

Function Method ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Fractional Complex Transform ◽

New Exact Solutions ◽

Non Linear ◽

De Vries

An improved extended tg-function method, which combines the fractional complex transform and the extended tanh-function method, is applied to find exact solutions of non-linear fractional partial differential equations. Generalized Hirota-Satsuma coupled Korteweg-de Vries equations are used as an example to elucidate the effectiveness and simplicity of the method.

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Analytical Solution of Fractional-Order Hyperbolic Telegraph Equation, Using Natural Transform Decomposition Method

Electronics ◽

10.3390/electronics8091015 ◽

2019 ◽

Vol 8 (9) ◽

pp. 1015 ◽

Cited By ~ 9

Author(s):

Hassan Khan ◽

Rasool Shah ◽

Dumitru Baleanu ◽

Poom Kumam ◽

Muhammad Arif

Keyword(s):

Applied Sciences ◽

Partial Differential Equations ◽

Differential Equations ◽

Fractional Order ◽

Decomposition Method ◽

Telegraph Equation ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Present Technique ◽

Telegraph Equations

In the current paper, fractional-order hyperbolic telegraph equations are considered for analytical solutions, using the decomposition method based on natural transformation. The fractional derivative is defined by the Caputo operator. The present technique is implemented for both fractional- and integer-order equations, showing that the current technique is an accurate analytical instrument for the solution of partial differential equations of fractional-order arising in all branches of applied sciences. For this purpose, several examples related to hyperbolic telegraph models are presented to explain the procedure of the suggested method. It is noted that the procedure of the present technique is simple, straightforward, accurate, and found to be a better mathematical technique to solve non-linear fractional partial differential equations.

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Fractional Green's function for fractional partial differential equations

Journal Européen des Systèmes Automatisés ◽

10.3166/jesa.42.639-651 ◽

2008 ◽

Vol 42 (6-8) ◽

pp. 639-651

Author(s):

Zaid Odibat ◽

Shaher Momani

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Green’S Function ◽

Green's Function ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Fractional Green’S Function

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Oscillation criteria of certain fractional partial differential equations

Advances in Difference Equations ◽

10.1186/s13662-019-2391-y ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 1

Author(s):

Di Xu ◽

Fanwei Meng

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Fractional Derivatives ◽

Sufficient Conditions ◽

Riccati Transformation ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Oscillation Criteria ◽

Generalized Riccati Transformation

Abstract In this article, we regard the generalized Riccati transformation and Riemann–Liouville fractional derivatives as the principal instrument. In the proof, we take advantage of the fractional derivatives technique with the addition of interval segmentation techniques, which enlarge the manners to demonstrate the sufficient conditions for oscillation criteria of certain fractional partial differential equations.

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