A sum operator method for the existence and uniqueness of positive solutions to Riemann–Liouville fractional differential equation boundary value problems

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

“…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].…”

The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems

“…This is because of both the intensive development of the theory of fractional calculus itself and the wide range of applications of such kind of equations in various scientific fields such as physics, mechanics, chemistry, economics, engineering and biological sciences, etc., see [18,20,21,28]. In recent years, the study of positive solutions for fractional differential equation boundary value problems has attracted considerable attention, and many results have been achieved, and here we refer the reader to [5,6,12,14,15,19,25,29,30,31,32,35,36,37] and the references therein for details.…”

“…These studies not only have theoretical significance but also have a wide range of applications in engineering, nuclear physics, biology, chemistry, technology, etc. Because of the crucial role played by nonlinear equations in applied science as well as mathematics, nonlinear functional analysis has been an active area of research, and nonlinear operators with connection to nonlinear (fractional) differential and integral equations have been extensively studied over the past several decades (see [5,6,12,14,15,19,25,29,30,31,32,35,36,37]). …”

“…Thereafter, many authors have investigated various kinds of nonlinear mixed monotone operators in Banach spaces such as nonlinear operators with concave-convex (see [4]), mixed monotone operators with α-concave-convex (see [33,34]), nonlinear operators with φ-concave-convex (see [10,26]), nonlinear operators with e-concave-convex (see [39]), and also obtained a lot of important results on mixed monotone operators (see [1,2,7,8,11,13,16,17,21,22,23,24,27,28,29,31,32,38]). These studies not only have theoretical significance but also have a wide range of applications in engineering, nuclear physics, biology, chemistry, technology, etc.…”

Existence results to certain functional equations in probabilistic Banach spaces with an application to integral equations

“…It is very important to know if such equations admit solutions and if a solution exists, it is unique. Many authors studied such questions and considered various classes of operator equations posed in a Banach space (see, for examples, [1,2,3,7,9,12,13,14,15,16]). In [8], we studied a class of operator equations posed in a probabilistic Banach space and involving decreasing and convex operators.…”