Abstract semilinear stochastic Itó-Volterra integrodifferential equations

Semilinear Volterra Integrodifferential Equations with Nonlocal Initial Conditions

where h ∈ L1(0,T ;X) and f : [0,T ]×X →X. This is obtained if one takes F(u)(t)= h(t)−∫ t 0 a(t−s)f (s,u(s))ds in (1.1). Such problems are important from the viewpoint of applications since they cover nonlocal generalizations of integrodifferential equations arising in the mathematical modeling of heat conduction in materials with memory. Byszewski [6, 7] initiated the work concerning abstract ...

Fractional Order Semilinear Volterra Integrodifferential Equations in Banach Spaces

In this paper, sufficient conditions are established for the existence results of fractional order semilinear Volterra integrodifferential equations in Banach spaces. The results are obtained by using the theory of fractional cosine families and fractional powers of operators.

Controllability of semilinear stochastic integrodifferential systems

Semilinear Volterra Integrodifferential Problems with Fractional Derivatives in the Nonlinearities

and Applied Analysis 3 is called the Riemann-Liouville fractional integral of h of order α > 0 when the right side exists. Here Γ is the usual Gamma function

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...