Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden–Fowler equations with initial and boundary conditions

Abstract

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.

On fractional hybrid and non-hybrid multi-term integro-differential inclusions with three-point integral hybrid boundary conditions

“…Now, we prove next result by using the approximate endpoint property for the set-valued map N which is defined in (11).…”

“…(C8) The operator N has the approximate endpoint property, where N is given in (11). Then the fractional non-hybrid inclusion problem (3) has a solution.…”

On the existence of solutions for a pointwise defined multi-singular integro-differential equation with integral boundary condition

“…Most researchers like to obtain numerical solutions of fractional differential equations specially singular ones (see foe example, [24,25] and [31]). It is natural that most softwares are not able to calculate solutions of most singular differential equations now while nowadays we can prove that most complicate problems such pointwise defined multi-singular fractional differential equations under some integral boundary conditions have solutions.…”

Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

“…Nonlocal problems concerning the conditions of the behavior of different classes of solutions play an important role in the qualitative theory of ordinary differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For more precision, we refer the readers to some specific problems such as boundedness, periodicity, almost periodicity, stability in the sense of Poisson and Ulam and to the problem of the existence of limit regimes of different types, convergence, dissipativity, and so on [17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”