Mild solutions of functional semilinear evolution Volterra integrodifferential equations on an unbounded interval

Fractional Cauchy problem with memory effects

“…Recently, the authors have obtained similar results for the nonlinear Volterra equation of convolution type see [1]. More results about mild solutions, blow up and critical nonlinearities appear in [14, 18, 25, 27, 28, 31–33] and the references therein.…”

Mild Solutions of Fractional Semilinear Integro-Differential Equations on an Unbounded Interval

“…into itself and has some other properties (see [6][7][8], for example). More generally, we can consider the operator I  on the function space  consisting of real functions being locally integrable over .…”

“…In order to solve (1), many different methods have been applied in the literature. Most of these methods use the notion of a measure of noncompactness in Banach spaces, see [6][7][8][9][10]. Such a method can be to apply in this work.…”

Local attractivity for integro-differential equations with noncompact semigroups

“…Evolution equations are used in many elds of applied mathematics [9,33].In recent years, this type of equation has gained a lot of attention [39].The theory of integro-di erential equations on in nite intervals plays a key role as it addresses certain real world problems; it has gained considerable attention recently and now represents an important nonlinear analysis branch. Broad applications for physics, mechanics, engineering, electric, chemistry, economy and other areas [2,6,35,36] have, in recent years, been found in integrodi erential equations; while numerous research papers and monographs have been written, devoting themselves to functional and integro-di erential equations [3,4,7,21,31,34,37]. Such documents contain speci c qualitative properties like existence, uniqueness, stability and asymptotic behavior of rst-order equations.…”