scholarly journals Numerical solution of two-dimensional fractional-order partial differential equations using hybrid functions

2021 ◽  
Vol 4 ◽  
pp. 100099
Author(s):  
Octavian Postavaru ◽  
Antonela Toma
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Order ◽  
Two Dimensional ◽  
Partial Differential ◽  
Hybrid Functions

scholarly journals Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Fukang Yin ◽  
Junqiang Song ◽  
Yongwen Wu ◽  
Lilun Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Approximate Solutions ◽  
Operational Matrices ◽  
Legendre Functions ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs). The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs). The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.

Simulation of Flow in a Rectangular Meandering Channel

2011 ◽  
Vol 130-134 ◽  
pp. 2688-2691
Author(s):  
K. Ma ◽  
W.L. Wei
Keyword(s):  
Experimental Data ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Coordinate System ◽  
Numerical Solution ◽  
Satisfactory Agreement ◽  
Two Dimensional ◽  
Complicated Shape ◽  
Partial Differential ◽  
Meandering Channel

This paper is concerned with the numerical solution of two-dimensional flows in a rectangular meandering channel. The technique of boundary-fitted coordinate system is used to overcome the difficulties resulting from the complicated shape of natural river boundaries; the method of physical fractional steps is used to solve the partial differential equations in the transformed plane. Comparison between computed and experimental data shows a satisfactory agreement.

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.

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