scholarly journals An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 505 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Analytical Technique ◽  
Full Support ◽  
Research Article ◽  
De Vries ◽  
Physical Phenomena

The Kortweg–de Vries equations play an important role to model different physical phenomena in nature. In this research article, we have investigated the analytical solution to system of nonlinear fractional Kortweg–de Vries, partial differential equations. The Caputo operator is used to define fractional derivatives. Some illustrative examples are considered to check the validity and accuracy of the proposed method. The obtained results have shown the best agreement with the exact solution for the problems. The solution graphs are in full support to confirm the authenticity of the present method.

scholarly journals Oscillation criteria of certain fractional partial differential equations

2019 ◽  
Vol 2019 (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.

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

2015 ◽  
Vol 19 (4) ◽  
pp. 1173-1176 ◽  
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.

scholarly journals Numerical Methods for Fractional Order Singular Partial Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Variable Coefficients ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

We implement relatively analytical methods, the homotopy perturbation method and the variational iteration method, for solving singular fractional partial differential equations of fractional order. The process of the methods which produce solutions in terms of convergent series is explained. The fractional derivatives are described in Caputo sense. Some examples are given to show the accurate and easily implemented of these methods even with the presence of singularities.

scholarly journals Semi-Analytic Technique for Solving Fractional Partial Differential Equations with Conformable Derivatives

2021 ◽  
Vol 24 (1) ◽  
pp. 39-44
Author(s):  
Noor I. Ibrahim ◽  
◽  
Osama H. Mohammed ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Approximate Methods ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Homotopy Analysis ◽  
Conformable Derivatives ◽  
Approximate Result

In this work, we present a semi-analytical technique to find an approximate result of the conformable fractional partial differential equations (CFPDEs). The fractional order derivative will be in the conformable (CFD) sense. This definition is effective and simple in the solution of the fractional differential equations that have intricate solution with classical fractional derivative definition like Riemann-Liouville and Caputo. Furthermore, the result obtained by the proposed technique is like those in previous studies that used other types of approximate methods like (Homotopy analysis method) but it has the advantage of being simpler than the rest of these methods. In addition, results demonstrate obtained the Precision and effectiveness of the suggested technique.

scholarly journals An efficient new iterative method for finding exact solutions of nonlinear time-fractional partial differential equations

2011 ◽  
Vol 16 (4) ◽  
pp. 403-414 ◽  
Author(s):  
Hüseyin Koçak ◽  
Ahmet Yıldırım
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Convergent Series ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Iterative Method

In this paper, a new iterative method (NIM) is used to obtain the exact solutions of some nonlinear time-fractional partial differential equations. The fractional derivatives are described in the Caputo sense. The method provides a convergent series with easily computable components in comparison with other existing methods.

scholarly journals Solving systems of multi-term fractional PDEs: Invariant subspace approach

2019 ◽  
Vol 10 (01) ◽  
pp. 1941010 ◽  
Author(s):  
Sangita Choudhary ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Fractional Derivatives ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Time And Space ◽  
Partial Differential ◽  
Fractional Pdes

In the present paper, invariant subspace method has been extended for solving systems of multi-term fractional partial differential equations (FPDEs) involving both time and space fractional derivatives. Further, the method has also been employed for solving multi-term fractional PDEs in [Formula: see text] dimensions. A diverse set of examples is solved to illustrate the method.

scholarly journals Application of Sinc-Galerkin Method for Solving Space-Fractional Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Sertan Alkan ◽  
Aydin Secer
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Fractional Derivatives ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Fractional Partial Differential Equations ◽  
Efficient Tool ◽  
Partial Differential ◽  
Fractional Boundary Value Problems

We employ the sinc-Galerkin method to obtain approximate solutions of space-fractional order partial differential equations (FPDEs) with variable coefficients. The fractional derivatives are used in the Caputo sense. The method is applied to three different problems and the obtained solutions are compared with the exact solutions of the problems. These comparisons demonstrate that the sinc-Galerkin method is a very efficient tool in solving space-fractional partial differential equations.

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