Improved ()-Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations

The fractional complex transformation is used to transform nonlinear partial differential equations to nonlinear ordinary differential equations. The improved ()-expansion method is suggested to solve the space and time fractional foam drainage and KdV equations. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

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APPLICATIONS OF FRACTIONAL COMPLEX TRANSFORM AND (G'/G)-EXPANSION METHOD FOR TIME-FRACTIONAL DIFFERENTIAL EQUATIONS

Journal of Applied Analysis & Computation ◽

10.11948/2016011 ◽

2016 ◽

Vol 6 (1) ◽

pp. 131-144 ◽

Cited By ~ 1

Author(s):

Ahmet Bekir ◽

◽

Ozkan Guner ◽

Mohammad Mirzazadeh ◽

◽

...

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Expansion Method ◽

Fractional Complex Transform ◽

Fractional Differential ◽

Time Fractional Differential Equations

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Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G ) $( \frac{G'}{G},\frac{1}{G} ) $ -expansion method

Advances in Difference Equations ◽

10.1186/s13662-018-1814-5 ◽

2018 ◽

Vol 2018 (1) ◽

Cited By ~ 6

Author(s):

Altaf A. Al-Shawba ◽

Farah A. Abdullah ◽

Khaled A. Gepreel ◽

Amirah Azmi

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Expansion Method ◽

Periodic Wave ◽

Periodic Wave Solutions ◽

Wave Solutions ◽

Higher Dimensional ◽

Fractional Differential ◽

Time Fractional Differential Equations

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Analytical solution of nonlinear space–time fractional differential equations using the improved fractional Riccati expansion method

Ain Shams Engineering Journal ◽

10.1016/j.asej.2014.10.014 ◽

2015 ◽

Vol 6 (2) ◽

pp. 613-620 ◽

Cited By ~ 14

Author(s):

Emad A-B. Abdel-Salam ◽

Elzain A.E. Gumma

Keyword(s):

Analytical Solution ◽

Differential Equations ◽

Fractional Differential Equations ◽

Expansion Method ◽

Space Time ◽

Fractional Differential ◽

Time Fractional Differential Equations

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Exact solutions of nonlinear fractional differential equations by ( G′/G )-expansion method

Chinese Physics B ◽

10.1088/1674-1056/22/11/110202 ◽

2013 ◽

Vol 22 (11) ◽

pp. 110202 ◽

Cited By ~ 82

Author(s):

Ahmet Bekir ◽

Özkan Güner

Keyword(s):

Differential Equations ◽

Exact Solutions ◽

Fractional Differential Equations ◽

Expansion Method ◽

Nonlinear Fractional Differential Equations ◽

Fractional Differential

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New exact solution for space-time fractional differential equations via (G′/G)-expansion method

Optik ◽

10.1016/j.ijleo.2016.10.116 ◽

2017 ◽

Vol 130 ◽

pp. 696-701 ◽

Cited By ~ 19

Author(s):

Ozkan Guner ◽

Hasan Atik ◽

Alzhanov Aytugan Kayyrzhanovich

Keyword(s):

Exact Solution ◽

Differential Equations ◽

Fractional Differential Equations ◽

Expansion Method ◽

Space Time ◽

Fractional Differential ◽

Time Fractional Differential Equations

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Application of $$\frac{G'}{G^2}$$ G ′ G 2 -Expansion Method for Solving Fractional Differential Equations

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-017-0344-2 ◽

2017 ◽

Vol 3 (S1) ◽

pp. 1415-1424 ◽

Cited By ~ 2

Author(s):

Nematollah Kadkhoda

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Expansion Method ◽

Fractional Differential

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New Exact Solutions of Fractional Differential Equations by (G′/G)-Expansion Method and Improved (G′/G)-Expansion Method

Generalized Fractional Order Differential Equations Arising in Physical Models ◽

10.1201/9780429430046-6 ◽

2018 ◽

pp. 145-181

Author(s):

Santanu Saha Ray ◽

Subhadarshan Sahoo

Keyword(s):

Differential Equations ◽

Exact Solutions ◽

Fractional Differential Equations ◽

Expansion Method ◽

New Exact Solutions ◽

Fractional Differential

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General solution of Bernoulli and Riccati fractional differential equations based on conformable fractional derivative

International Journal of Applied Mathematical Research ◽

10.14419/ijamr.v6i2.7014 ◽

2017 ◽

Vol 6 (2) ◽

pp. 49 ◽

Cited By ~ 13

Author(s):

Zainab Ayati ◽

Jafar Biaar ◽

Mousa Ilei

Keyword(s):

General Solution ◽

Differential Equations ◽

Fractional Derivative ◽

Ordinary Differential Equations ◽

Fractional Differential Equations ◽

Riccati Equations ◽

Nonlinear Ordinary Differential Equations ◽

Conformable Fractional Derivative ◽

Numerical Examples ◽

Fractional Differential

This paper is aimed to develop two well-known nonlinear ordinary differential equations, Bernoulli and Riccati equations to fractional form. General solution to fractional differential equations are detected, based on conformable fractional derivative. For each equation, numerical examples are presented to illustrate the proposed approach.

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