Positive Solutions for a Class of p-Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems

Abstract

In this paper, using the Avery–Henderson fixed point theorem and the monotone iterative technique, we investigate the existence of positive solutions for a class of p-Laplacian Hadamard fractional-order three-point boundary value problems.

The Nehari manifold for aψ-Hilfer fractionalp-Laplacian

“…Results on the existence and multiplicity of solutions for nonlinear boundary value problems of fractional differential equations in a fractional derivative space can be found in [16,17,18,19,33,41]. Ledesma [20,21,22] and others discuss variational problems via fractional derivatives and integrals, with important techniques, such as the Mountain Pass Theorem, Nehari manifolds, critical point theory and fibering maps (see [17,23,24,36,37,40,42]).…”

Controllability of Impulsive ψ-Caputo Fractional Evolution Equations with Nonlocal Conditions

“…It turns out that fractional calculus can provide a more vivid and accurate description of many practical problems than integral ones. Increasingly more recent achievements in various aspects of science and technology have proved that fractional differential systems [15][16][17][18][19][20] have naturally replaced integer-order differential systems. What makes fractional calculus special is the fact that there exist various kinds of fractional operators which can be chosen to provide a more accurate modeling of real-world phenomena.…”

Explicit monotone iterative sequences for positive solutions of a fractional differential system with coupled integral boundary conditions on a half-line

“…Fractional-order differential equations is a natural generalization of the case of integer order, which has become the focus of attention involving various kinds of boundary conditions because of the wide application in mathematical models and applied sciences. Some latest results on the topic can be found in a series of papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references therein. In particular, a monotone iterative technique is believed to be an efficient and important method to deal with sequences of monotone solutions for initial and boundary value problems.…”