scholarly journals The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohamed S. Abdel Latif ◽  
Abass H. Abdel Kader ◽  
Dumitru Baleanu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Fractional Derivatives ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Generalized Fractional Derivatives

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.

The Invariant Subspace Method for Solving Fractional Partial Differential Equations

2020 ◽  
pp. 267-282
Author(s):  
Mohamed Soror Abdel Latif ◽  
Abass Hassan Abdel Kader
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Balance Principle ◽  
New Exact Solutions

In this chapter, the authors discuss the effectiveness of the invariant subspace method (ISM) for solving fractional partial differential equations. For this purpose, they have chosen a nonlinear time fractional partial differential equation (PDE) with variable coefficients to be investigated through this method. One-, two-, and three-dimensional invariant subspace classifications have been performed for this equation. Some new exact solutions have been obtained using the ISM. Also, the authors give a comparison between this method and the homogeneous balance principle (HBP).

scholarly journals Invariant subspace method: A tool for solving fractional partial differential equations

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Sangita Choudhary ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Subspace ◽  
Caputo Derivative ◽  
Linear Time ◽  
Subspace Method ◽  
Fractional Partial Differential Equations ◽  
Time And Space ◽  
Partial Differential ◽  
Non Linear

AbstractIn this paper invariant subspace method has been employed for solving linear and non-linear time and space fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the effectiveness and applicability of the method.

scholarly journals A modified invariant subspace method for solving partial differential equations with non-singular kernel fractional derivatives

2020 ◽  
Vol 5 (2) ◽  
pp. 35-48 ◽  
Author(s):  
Kamal Ait Touchent ◽  
Zakia Hammouch ◽  
Toufik Mekkaoui
Keyword(s):  
Partial Differential Equations ◽  
Numerical Methods ◽  
Differential Equations ◽  
Exact Solutions ◽  
Invariant Subspace ◽  
Fractional Derivatives ◽  
Subspace Method ◽  
Partial Differential ◽  
Singular Kernels ◽  
Fractional Differential

AbstractIn this work, the well known invariant subspace method has been modified and extended to solve some partial differential equations involving Caputo-Fabrizio (CF) or Atangana-Baleanu (AB) fractional derivatives. The exact solutions are obtained by solving the reduced systems of constructed fractional differential equations. The results show that this method is very simple and effective for constructing explicit exact solutions for partial differential equations involving new fractional derivatives with nonlocal and non-singular kernels, such solutions are very useful to validate new numerical methods constructed for solving partial differential equations with CF and AB fractional derivatives.

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 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 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.

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