In this paper, we establish some new properties of (?,c)-periodic and asymptotically functions, then apply them to study the existence uniqueness mild solutions these types following semilinear fractional differential equations: (1) {cDt?u(t)=Au(t)+cDt??1f(t,u(t)),1<?<2,t?R,u(0)=0(1) (2) {cDt?u(t)=Au(t)+cDt??1f(t,u(t?h)),1<?<2,t,h?R+,u(0)=0(2) where cDt?(?)(1<?<2) stands for Caputo derivative A...

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Abstract In this paper, the existence of solutions for differential inclusions of fractional order q ∈ (1, 2] with nonlocal strip conditions is investigated. Our study includes two cases: (i) the multivalued map involved in the problem is not ...

where t ∈ T = [ν – β – 1,b + ν – β – 1]Nν–β–1 . βν–2, b∇ν are left and right fractional difference operators, respectively, and φp(s) = |s|p–2s, p > 1. By using the method of upper and lower solution and the Schauder fixed point theorem, we obtain the existence of positive solutions for the above boundary value problem; and applying a monotone iterative technique, we establish iterative schemes...

*Correspondence: [email protected] 1Institute of Mathematics, Jilin University, Changchun, China 2Fundamental Department, Aviation University of Air Force, Changchun, 130000, China Abstract This paper is mainly devoted to studying one kind of the second order differential equation. Under periodic-integrable boundary value condition, the existence of the solutions of this equation is discussed ...

This paper deals with the approximate controllability of a functional differential equation with deviated argument and finite delay. Sufficient condition for approximate controllability is proved under the assumption that the linear control system is approximately controllable; thereby removing the need to assume the invertibility of a controllability operator which fails to exist in infinite d...

We consider the pair diffusion process which includes cluster reactions of high order. We are able to prove a local (in time) existence result in arbitrary space dimensions. The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic equation for the electrochemical potential. The l...

In this paper concerns the third-order boundary-value problem u′′′(t) + f(t, u(t), u′(t), u′′(t)) = 0, 0 < t < 1, r1u(0)− r2u(0) = r3u(1) + r4u(1) = u′′(0) = 0. By placing certain restrictions on the nonlinear term f , we prove the existence of at least one solution to the boundary-value problem with the use of lower and upper solution method and of Schauder fixed-point theorem. The constructio...

Impulsive Cohen-Grossberg neural networks with bounded and unbounded delays i.e., mixed delays are investigated. By using the Leray-Schauder fixed point theorem, differential inequality techniques, and constructing suitable Lyapunov functional, several new sufficient conditions on the existence and global exponential stability of periodic solution for the system are obtained, which improves som...

The three-dimensional compressible magnetohydrodynamic isentropic flow with zero magnetic diffusivity is studied in this paper. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field. The existence and uniqueness of local-in-time strong solutions with large initial data is established. Strong solutions have weaker regularity than ...

This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigat...