Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions

On a coupled system of fractional differential equations with nonlocal non-separated boundary conditions

“…where c D α denotes the Caputo fractional derivative of order α, f is a continuous function on [0, T] × R and a i , b i , c i , i = 1, 2 are real constants such that a 1 + b 1 = 0 and b 2 = 0. The system of fractional differential equations boundary value problems has also received much attention and its research has developed very rapidly; see [2,4,5,8,10,12,13,20,21,25,[31][32][33]35]. Recently, Alsulalt et al [13] established the existence and uniqueness results for a nonlinear coupled system of Caputo type fractional differential equations supplemented with non-separated coupled boundary conditions.…”

Multi-Term Fractional Differential Equations with Generalized Integral Boundary Conditions

“…Fractional-order initial and boundary value problems, involving different kinds of derivatives such as Riemann-Liouville, Caputo, and Hadamard type, have been studied by many authors. The literature on the topic is rapidly augmented with a variety of interesting and useful results during the past few years (see, for instance, [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and references therein).…”

Unique solutions for a new coupled system of fractional differential equations

“…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. Recently, several papers [4,[8][9][10] considered some new coupled systems of fractional differential equations and obtained some new results about the existence and uniqueness of solutions by using general methods.…”

“…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.…”