Multiple positive solutions for mixed fractional differential system with p-Laplacian operators

Abstract

This paper is focused on researching a class of mixed fractional differential system with p-Laplacian operators. Based on the properties of the corresponding Green's function, different combinations of superlinearity or sublinearity for the nonlinearities and other appropriate conditions, the existence of multiple positive solutions are derived via the Guo-Krasnosel'skii fixed point theorem. An example is then given to illustrate the usability of the main results. MSC: 26A33; 34B18Keywords: Multiple positive solutions; Mixed fractional differential system; p-Laplacian operators; Coupled integral boundary conditions 1 0 a(s)v(s) dA 1 (s), 1 0 b(s)u(s) dA 2 (s) denote the Riemann-Stieltjes integrals with a signed measure, that is A i : [0, 1] → [0, +∞) is the function of bounded variation. a, b : [0, 1] → [0, +∞) are continuous, f i : [0, 1] × [0, +∞) × [0, +∞) → [0, +∞) is a continuous function, i = 1, 2.Compared with the integer order systems, fractional differential systems are regarded as a better tool in the description of some problems in science and engineering. Arafal et

Positive Solutions for a System of p-Laplacian Equation Involving Integral Boundary Conditions

“…Multipoint boundary value problems for differential equations have played an important role in mathematics. Due to the development of fractional order theory and the successful applications of the fractional order which are applied in many fields, such as signal analysis and processing, and medical image edge information detection, many results about the existence of solutions of coupled system fractional differential equation with integral boundary conditions have already published [1][2][3][4][5]9]. What's more, some academicians study the existence of solutions for nonlinear fractional differential equations with integral boundary conditions [6][7][8].…”

Multiple Positive Solutions for a System of Caputo Fractionalp-Laplacian Boundary Value Problems

“…Recently, coupled systems of fractional differential equations have also been investigated by many authors. Some results on the direction can be found in a series of papers [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and the references cited therein.…”

“…In [11], Wang utilized the Guo-Krasnosel'skii fixed point theorem to investigate the multiple positive solutions for the mixed fractional p-Laplacian differential system:…”