Iterative approximation of positive solutions for fractional boundary value problem on the half-line

Abstract

In this paper, an iterative method is applied to solve some p-Laplacian boundary value problem involving Riemann-Liouville fractional derivative operator. More precisely, we establish the existence of two positive solutions. Moreover, we prove that these solutions are one maximal and the other is minimal. An example is presented to illustrate our main result. Finally, a numerical method to solve this problem is given.

Existences Results for Some Nonsingular $p$-Kirchhoff Problems with $\psi$-Hilfer Fractional Derivative

“…Because fractional differential operators are very important, several papers involving different derivatives, we cite for instance the papers of Ben Ali et al [5], Chamekh et al [29], Ghanmi and Horrigue [31,32], Horrigue [34], Torres [25], and Wang et al [43].…”

Existence Results for a Class of Nonlinear Hadamard Fractional with p-Laplacian Operator Differential Equations

“…For details and recent developments on Hadamard fractional differential equations, see (Huang and Liu, 2018;Wang et al, 2018;Zhai et al, 2018) and references therein. Recently, some researches have extensively interested in the study of the fractional differential equations with p-Laplacian operators see for examples (Chamekh et al, 2018;Ding et al, 2015).…”