Existence of asymptotically almost automorphic solutions for a third order differential equation

Existence of Asymptotically Almost Automorphic Solutions for a Third Order Differential Equation

This paper deals with results on existence of asymptotically almost automorphic solutions for a third order in time abstract differential equation which model, on one side, high intensity ultrasound in acoustic wave propagation, while on the other side, vibrations of flexible structures possessing internal material damping. We established the asymptotically almost automorphy of the output solut...

Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp-Pseudo Almost Automorphic Coefficients

Asymptotically almost automorphic solutions of fractional order neutral integro-differential equations

In this paper, we study the existence of asymptotic almost automorphic solution of fractional neutral integro-differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz condition on the forcing term. Finally examples are given to illustrate the analytical findings. Mathematics Subject Classification(2010): 34A08, 1...

Existence of Almost Automorphic Solutions to Some Classes of Nonautonomous Higher-order Differential Equations

In this paper, we obtain the existence of almost automorphic solutions to some classes of nonautonomous higher order abstract differential equations with Stepanov almost automorphic forcing terms. A few illustrative examples are discussed at the very end of the paper.

Existence of Solutions for a Nonlinear Fractional Order Differential Equation

Let D denote the Riemann-Liouville fractional differential operator of order α. Let 1 < α < 2 and 0 < β < α. Define the operator L by L = D − aD where a ∈ R. We give sufficient conditions for the existence of solutions of the nonlinear fractional boundary value problem Lu(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) = 0.