scholarly journals A new approach for solving a system of fractional partial differential equations

2013 ◽  
Vol 66 (5) ◽  
pp. 838-843 ◽  
Author(s):  
H. Jafari ◽  
M. Nazari ◽  
D. Baleanu ◽  
C.M. Khalique
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Approach

scholarly journals A New Approach for Solving Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dimensional Space ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Approach ◽  
New Exact Solutions ◽  
Biological Population ◽  
Complex Transformation ◽  
Dimensional Space Time

We propose a new approach for solving fractional partial differential equations based on a nonlinear fractional complex transformation and the general Riccati equation and apply it to solve the nonlinear time fractional biological population model and the (4+1)-dimensional space-time fractional Fokas equation. As a result, some new exact solutions for them are obtained. This approach can be suitable for solving fractional partial differential equations with more general forms than the method proposed by S. Zhang and H.-Q. Zhang (2011).

A new clique polynomial approach for fractional partial differential equations

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Waleed Adel ◽  
Kumbinarasaiah Srinivasa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Current Approach ◽  
Polynomial Method ◽  
Algebraic Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Approach ◽  
Novel Approach ◽  
Grid Points

Abstract This paper generates a novel approach called the clique polynomial method (CPM) using the clique polynomials raised in graph theory and used for solving the fractional order PDE. The fractional derivative is defined in terms of the Caputo fractional sense and the fractional partial differential equations (FPDE) are converted into nonlinear algebraic equations and collocated with suitable grid points in the current approach. The convergence analysis for the proposed scheme is constructed and the technique proved to be uniformly convegant. We applied the method for solving four problems to justify the proposed technique. Tables and graphs reveal that this new approach yield better results. Some theorems are discussed with proof.

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.

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