Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations

Abstract

In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to obtain conditions for the existence and uniqueness of positive solutions. We discuss Hyers-Ulam (HU) type stability of the concerned solutions and provide an example for illustration of the obtained results.

Study of implicit delay fractional differential equations under anti-periodic boundary conditions

“…In this regard a lot of research work can be found in the literature about existence theory. We refer the readers to [11][12][13][14]. On the other hand, the area devoted to establishing a procedure for numerical solutions has been investigated very well.…”

Existence and uniqueness of positive solutions for a new class of coupled system via fractional derivatives

“…A lot of fractional differential equations and coupled systems have been studied widely; see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]24] and the references therein. As is well known, coupled systems with boundary conditions appear in the investigations of many problems such as mathematical biology (see [9,30]), natural sciences and engineering; for example, we can see beam deformation and steady-state heat flow (see [25,26]) and heat equations (see [18,24]).…”

“…So the subject of coupled systems is gaining much attention and importance. There are a large number of articles dealing with the existence or multiplicity of solutions or positive solutions for some nonlinear coupled systems with boundary conditions; for details, see [7,8,10,11,20,21,27,29,32,33,[35][36][37][38][39][40][41].…”

Exponential behavior of neutral impulsive stochastic integro-differential equations driven by Poisson jumps and Rosenblatt process

“…Several authors have considered the existence, uniqueness and asymptotic behavior of mild solutions, and many important theory and applications ndings have been obtained. For more details we refer to the papers by Ali et al [4], El-Borai et al [11], Gorec and Sathanantham [12], Gupta and Dabas [15], Gupta and al. [16], Laksmikantha [22], Ahmed [2], Ahmed et al [3], Arthi and Balachandran [5],Gupta et al [14], Levin et al [24].…”