Abstract Volterra Integro-Differential Equations

PREFACE NOTATION INTRODUCTION PRELIMINARIES Vector-valued functions, closed operators and integration in sequentially complete locally convex spaces Laplace transform in sequentially complete locally convex spaces Operators of fractional differentiation, Mittag-Leffler and Wright functions (a k)-REGULARIZED C-RESOLVENT FAMILIES IN LOCALLY CONVEX SPACES Definition and main structural properties of (a k)-regularized C-resolvent families Wellposedness of related abstract Cauchy problems Convoluted C-semigroups and convoluted C-cosine functions in locally convex spaces Differential and analytical properties of (a k)-regularized C-resolvent families Systems of abstract time-fractional equations q-Exponentially equicontinuous (a k)-regularized C-resolvent families Abstract differential operators generating fractional resolvent families Perturbation theory for abstract Volterra equations Bounded perturbation theorems Unbounded perturbation theorems Time-dependent perturbations of abstract Volterra equations Approximation and convergence of (a k)-regularized C-resolvent families (a k)-Regularized (C1 C2)-existence and uniqueness families Complex powers of (a b C)-nonnegative operators and fractional resolvent families generated by them Complex powers of a C-sectorial operator A satisfying 0 2 (C(A)) The Balakrishnan operators Complex powers of almost C-nonnegative operators The case m = 1 Semigroups generated by fractional powers of almost C-sectorial operators Fractional powers of (a b C)-nonnegative operators and semigroups generated by them The existence and growth of mild solutions of operators generating fractionally integrated C-semigroups and cosine functions in locally convex spaces Representation of powers Abstract multi-term fractional differential equations k-Regularized (C1 C2)-existence and uniqueness propagation families for (2) k-Regularized (C1 C2)-existence and uniqueness families for (2) Approximation and convergence of k-regularized C-resolvent propagation families further results, examples and applications (a k)-Regularized C-resolvent families and abstract multi-term fractional differential equations HYPERCYCLIC AND TOPOLOGICALLY MIXING PROPERTIES OF CERTAIN CLASSES OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS Hypercyclic and topologically mixing properties of abstract rst order equations Disjoint hypercyclic semigroups Hypercyclic and topologically mixing properties of abstract second order equations C-Distribution cosine functions, almost C-distribution cosine functions and integrated C-cosine functions Hypercyclicity and chaos for C-distribution cosine functions and integrated C-cosine functions Hypercyclic and chaotic properties of cosine functions Disjoint hypercyclicity of C-distribution cosine functions Hypercyclic and topologically mixing properties of abstract multi-term fractional differential equations Hypercyclic and topologically mixing properties of -times C-regularized resolvent families Hypercyclic and topologically mixing properties of solutions of (2) with Aj = cjI cj 2 C j 2 Nn1 Topological dynamics of certain classes of abstract time-fractional PDEs with unilateral backward shifts Index