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Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden-Fowler equations with initial and boundary conditions. (English) Zbl 1452.65373

Summary: In this paper, we have applied an iterative method to the singular and nonlinear fractional partial differential of Emden-Fowler equations types. Haar wavelets operational matrix of fractional integration will be used to solve the problem with the Picard technique. The singular equations turn to Sylvester equations that will be solved so that numerically solvable is very cost-effective. Moreover, the proposed technique is reliable enough to overcome the difficulty of the singular point at \(x = 0\). Numerical examples are providing to illustrate the efficiency and accuracy of the technique.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35R11 Fractional partial differential equations
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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