A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

Abstract

This paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder's alternative, whereas the uniqueness of solution is established by Banach's contraction principle. An illustrative example is also included.MSC 2010 : Primary 34A08; Secondary 34A12, 34B15

Nonlocal boundary value problems for fractional differential inclusions with Erdélyi-Kober fractional integral boundary conditions

“…For further details and examples see Refs. [5][6][7][8][9][10]. For some recent development of the topic see Refs.…”

Unique solutions for a new coupled system of fractional differential equations

“…Different boundary conditions of coupled systems can be found in the discussions of some problems such as Sturm-Liouville problems and some reaction-diffusion equations (see [26,27]), and they have some applications in many fields such as mathematical biology (see [28,29]), natural sciences and engineering; for example, we can see beam deformation and steady-state heat flow [30,31] and heat equations [14,32,33]. So nonlinear coupled systems subject to different boundary conditions have been paid much attention to, and the existence or multiplicity of solutions for the systems has been given in literature, see [4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][22][23][24][25] for example. The usual methods used are Schauder's fixed point theorem, Banach's fixed point theorem, Guo-Krasnosel'skii's fixed point theorem on cone, nonlinear differentiation of Leray-Schauder type and so on.…”

Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

“…Recently, more studies have looked at the boundary value problems of nonlinear Hadamard fractional differential equations [15][16][17][18] . Ahmad and Ntouyas 19,20 studied the existence and uniqueness of solutions for fractional integral boundary value problem involving Hadamard-type fractional differential equations/systems with integral boundary conditions by applying some standard fixed point theorems.…”