Existence and controllability results for impulsive partial functional differential inclusions

In this paper we prove the existence and the controllability of mild and extremal mild solutions for first-order semilinear densely defined impulsive functional differential inclusions in separable Banach spaces with local and nonlocal conditions.     

Some Uniqueness Results on Controllability for Functional Semilinear Differential Equations in Fréchet Spaces

In this paper, a recent nonlinear alternative for contraction maps in Fréchet spaces, due to Frigon and Granas, is combined with semigroup theory and used for the investigation of the controllability of some classes of semilinear functional and neutral functional differential equations in Banach spaces on a semiinfinite interval.     

Electron Transfer in the Cs⊂{Mn4Fe4} Cubic Switch: A Soluble Molecular Model of the MnFe Prussian‐Blue Analogues

A mixed‐valence {Mn^II₃Mn^IIIFe^II₂Fe^III₂} cyanide‐bridged molecular cube hosting a caesium cation, Cs?{Mn₄Fe₄}, was synthesized and structurally characterized by X‐ray diffraction. Cyclic‐voltammetry measurements show that its electronic state can be switched between five different redox states, which results in a remarkable electrochromic effect. Magnetic measurements on fresh samples point to the occurrence of a spin‐state change near room temperature, which could be ascribed to a metal‐to‐metal electron transfer converting the {Fe^II?CN?Mn^III} pair into a {Fe^III?CN?Mn^II} pair. This feature was only previously observed in the polymeric MnFe Prussian‐blue analogues (PBAs). Moreover, this novel switchable molecule proved to be soluble and stable in organic solvents, paving the way for its integration into advanced materials.     

Boundary Value Problems for Nonlinear Implicit Caputo–Hadamard-Type Fractional Differential Equations with Impulses

In this paper, the authors establish the existence and uniqueness of solutions for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and Caputo–Hadamard type fractional derivatives. The stability of this problem is also studied. The arguments are based on the Banach contraction principle and Schaefer’s fixed point theorem. Two examples are presented to show the applicability of the results.     

Controllability for Functional Differential and Integrodifferential Inclusions in Banach Spaces

In this paper, we establish sufficient conditions for the controllability of functional differential and integrodifferential inclusions in Banach spaces. We rely on a fixed-point theorem for condensing maps due to Martelli.     

Controllability of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions

In this paper, we establish sufficient conditions for the controllability ofsecond-order differential inclusions in Banach spaces with nonlocalconditions. We rely on a fixed-point theorem for condensing maps due toMartelli.     

Darboux problem for impulsive partial hyperbolic differential equations of fractional order with variable times and infinite delay

This paper deals with the existence of solutions to impulsive partial functional differential equations with impulses at variable times and infinite delay, involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray–Schauder type.