Abstract
By using a nonlinear method, we try to solve partial fractional differential equations. In this way, we construct the Laguerre wavelets operational matrix of fractional integration. The method is proposed by utilizing Laguerre wavelets in conjunction with the Adomian decomposition method. We present the procedure of implementation and convergence analysis for the method. This method is tested on fractional Fisher’s equation and the singular fractional Emden–Fowler equation. We compare the results produced by the present method with some well-known results.
Highlights
The fractional calculus has been extended extremely and investigated in distinct areas and applications by many research works
By developing the Laguerre wavelets collocation method and using the Adomian decomposition technique, our aim is the investigation of the partial fractional differential equation
4 Method of solution we review the method for the partial fractional differential equation
Summary
The fractional calculus has been extended extremely and investigated in distinct areas and applications by many research works (see, for example, [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]). In 1937, Fisher, Kolmogorov, Petrovsky, and Piscounov investigated independently the Fisher-KPP equation (or Fisher’s equation; see [21, 22]). As you know, this equation is about population dynamics to describe the spatial spread of an advantageous allele and explores its traveling wave solutions. There are some chemical and biological applications for this famous equation and its fractional version (see, for example, [34,35,36]).
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