Positive solutions to fractional boundary-value problems with p-Laplacian on time scales

Abstract

In this article, we consider the following boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator:where 1 < α ≤ 2 is a real number, the time scale T is a nonempty closed subset of R. MSC: 34B15

Positive solutions of fractional p-Laplacian equations with integral boundary value and two parameters

“…Fractional p-Laplacian equations are becoming more and more important, they can be used to describe a class of diffusion phenomena, which have been widely used in the fields of fluid mechanics, material memory, biology, plasma physics, finance and chemistry. Many important results related to the boundary value problems of fractional differential equations with p-Laplacian operator have been obtained; see [14][15][16][17][18][19][20][21][22][23][24]. But in practical problems, disturbance is objective.…”

Iterative positive solutions to a coupled fractional differential system with the multistrip and multipoint mixed boundary conditions

“…In the past few years the fractional boundary value problems are found to be popular in the research community because of their numerous applications in many disciplinary areas, such as optics, thermal, mechanics, control theory, nuclear physics, economics, signal and image processing, medicine, and so on [1][2][3][4]. To meet the practical application needs, many different theoretical approaches have been taken to study the existence, uniqueness, and multiplicity of solutions to fractional-order boundary value problems, for instance, the method of upper and lower solutions [5][6][7][8][9], the fixed point theory [10][11][12][13], the monotone iterative technique [14][15][16][17][18][19], the coincidence degree theory [20][21][22], etc. In comparison, the monotone iterative technique has more advantages, such as it not only proves the existence of positive solutions but also can obtain approximate solutions that can meet different accuracy requirements.…”

Asymptotical stabilization of the nonlinear upper triangular fractional-order systems

“…Fractional-order systems (FOS) have received a great deal of attention from mathematicians, physicists, chemists, biologists, and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. It has been the huge development of the theory and the applications in many fields, especially in control.…”