scholarly journals A New Analytical Technique to Solve System of Fractional-Order Partial Differential Equations

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 150037-150050 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Umar Farooq ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Partial Differential ◽  
Analytical Technique

scholarly journals Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 532 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Poom Kumam ◽  
Muhammad Arif ◽  
Dumitru Baleanu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Present Article ◽  
Fractional Order ◽  
Present Method ◽  
Decomposition Method ◽  
Proportional Delay ◽  
Partial Differential ◽  
Analytical Technique ◽  
In Series

In the present article, fractional-order partial differential equations with proportional delay, including generalized Burger equations with proportional delay are solved by using Natural transform decomposition method. Natural transform decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. Therefore, Natural transform decomposition method is considered to be one of the best analytical technique, to solve fractional-order linear and non-linear Partial deferential equations particularly fractional-order partial differential equations with proportional delay.

Invariant solutions of fractional-order spatio-temporal partial differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nkosingiphile Mnguni ◽  
Sameerah Jamal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Growth Models ◽  
Spatial Patterning ◽  
Partial Differential ◽  
Symmetry Approach ◽  
Time Component ◽  
Spatio Temporal ◽  
Lie Symmetry Approach

Abstract This paper considers two categories of fractional-order population growth models, where a time component is defined by Riemann–Liouville derivatives. These models are studied under the Lie symmetry approach, and we reduce the fractional partial differential equations to nonlinear ordinary differential equations. Subsequently, solutions of the latter are determined numerically or with the aid of Laplace transforms. Graphical representations for integral and trigonometric solutions are presented. A key feature of these models is the connection between spatial patterning of organisms versus competitive coexistence.

scholarly journals Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Yongjin Li ◽  
Kamal Shah
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Coupled Systems ◽  
Test Problems ◽  
Operational Matrices ◽  
Partial Differential ◽  
Established Technique

We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique.

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