Positive solutions for a boundary value problem of fractional differential equation with p-Laplacian operator

Abstract

In this paper, the existence of a positive solution to a boundary value problem of fractional differential equations with the p-Laplacian operator is studied. By applying a monotone iterative method, some existence results of positive solutions are obtained. In addition, an example is included to illustrate the main results.

Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain

“…In addition, in this paper, we consider the timefractional derivative is the Caputo fractional derivative of order 0 < α < 1, but in Ref. [45][46][47][48][49][50][51][52], one mentioned the Caputo-Fabrizio fractional integro-differential equation, which is very useful in practice. We will consider the inverse problem of Caputo-Fabrizio fractional integro-differential equations, and use the Tikhonov regularization method to solve this inverse problem.…”

Monotone iterative method for fractional p-Laplacian differential equations with four-point boundary conditions

“…On the other hand, BVPs involving p-Laplacian have attracted a lot of attention during the last decades (see, for example, [16][17][18][19]). Also, we refer to [20][21][22][23][24][25][26][27][28], where BVPs for FrDE involving the p-Laplacian were considered. References [22,25,28], where the fourpoint BVPs were considered, are of our special interest.…”

“…Also, we refer to [20][21][22][23][24][25][26][27][28], where BVPs for FrDE involving the p-Laplacian were considered. References [22,25,28], where the fourpoint BVPs were considered, are of our special interest. In [25], Wang with α, β ∈ R; 1 < α, β ≤ 2; 0 ≤ a, b ≤ 1; 0 < ξ , η < 1.…”

Multiplicity of positive solutions for Hadamard fractional differential equations with p-Laplacian operator

“…Recently, many scholars have paid more attention to the fractional differential equation boundary value problems and associated with p-Laplacian operator, see [15][16][17][18][19][20][21][22][23][24][25][26][27].…”

“…In [26] Tian et al considered the boundary value problem of fractional differential equations with p-Laplacian operator ⎧ ⎨ ⎩ D γ (φ p (D α u(t))) = f (t, u(t)), 0 < t < 1,…”