Multiple Positive Solutions for a Class of Boundary Value Problem of Fractional p , q -Difference Equations under p , q -Integral Boundary Conditions

This paper is mainly concerned with a class of fractional p , q -difference equations under p , q -integral boundary conditions. Multiple positive solutions are established by using the topological degree theory and Krein–Rutman theorem. Finally, two examples are worked out to illustrate the main results.

Periodic Third-Order Problems with a Parameter

This work concerns with the solvability of third-order periodic fully problems with a weighted parameter, where the nonlinearity must verify only a local monotone condition and no periodic, coercivity or super or sublinearity restrictions are assumed, as usual in the literature. The arguments are based on a new type of lower and upper solutions method, not necessarily well ordered. A Nagumo growth condition and Leray–Schauder’s topological degree theory are the existence tools. Only the existence of solution is studied here and it will remain open the discussion on the non-existence and the multiplicity of solutions. Last section contains a nonlinear third-order differential model for periodic catatonic phenomena, depending on biological and/or chemical parameters.

Existence of solutions for a coupled system of fractional differential equations by means of topological degree theory

This paper investigates the existence of solutions for a coupled system of fractional differential equations. The existence is proved by using the topological degree theory, and an example is given to show the applicability of our main result.

Dynamic behaviors for inertial neural networks with reaction-diffusion terms and distributed delays

A class of inertial neural networks (INNs) with reaction-diffusion terms and distributed delays is studied. The existence and uniqueness of the equilibrium point for the considered system is obtained by topological degree theory, and a sufficient condition is given to guarantee global exponential stability of the equilibrium point. Finally, an example is given to show the effectiveness of the results in this paper.

Study of an implicit type coupled system of fractional differential equations by means of topological degree theory

In this work, a sufficient condition required for the presence of positive solutions to a coupled system of fractional nonlinear differential equations of implicit type is studied. To study sufficient conditions essential for the existence of unique solution degree theory is used. Two examples are given to illustrate the established results.

Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions

This paper is concerned with a class of implicit-type coupled system with integral boundary conditions involving Caputo fractional derivatives. First, the existence result of solutions for the considered system is obtained by means of topological degree theory. Next, Ulam–Hyers stability and generalized Ulam–Hyers stability are studied under some suitable assumptions. Finally, one example is worked out to illustrate the main results.