11 Results Found

This paper develops the theory of strongly continuous semigroups and abstract evolution equations in modular function spaces. We study the autonomous problem $\dot{u}\left(t\right)=Bu\left(t\right)$ with initial condition $u\left(0\right)=u_0\in L_{\rho }$, where B is the infinitesimal ge...

This paper studies the properties of the evolution operators of a class of time-delay systems with linear delayed dynamics. The considered delayed dynamics may, in general, be time-varying and associated with a finite set of finite constant point del...

An alternative approach is proposed for constructing a strongly continuous semigroup based on the classical method of successive approximations, or Picard iterations, together with generating functions. An application to a Black–Scholes integro-diffe...

This paper investigates the uniform continuity and strong continuity of the semigroups of the fractional integral operators of power functions. Using the Krasnoselskii’s fixed-point theorem, we have studied the non-local problem related to frac...

The fractional order differential equation \(u'(t)=Au(t)+\gamma D_t^{\alpha} Au(t)+f(t), \ t>0\), \(u(0)=a\in X\) is studied, where \(A\) is an operator generating a strongly continuous one-parameter semigroup on a Banach space \(X\), \(D_t^{\alp...

Herein, we investigated the controllability of a semilinear multi-valued differential equation with non-instantaneous impulses of order $\alpha \in (1,2)$, where the linear part is a strongly continuous cosine family without compactness. We did not assume any c...

In this paper, we establish sufficient conditions for the existence of mild solutions for certain impulsive evolution differential equations with causal operators in separable Banach spaces. We rely on the existence of mild solutions for the strongly...

In the qualitative theory of differential equations in Banach spaces, the resolving families of operators of such equations play an important role. We obtained necessary and sufficient conditions for the existence of strongly continuous resolving fam...

We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroup...

In this paper, we derive sufficient conditions that guarantee an description of long-time asymptotic behavior of the solution to the Cauchy problem governed by a linear neutron transport equation with a partially elastic collision operator under peri...

Stiff delay differential equations are frequently utilized in practice, but their numerical simulations are difficult due to the complicated interaction between the stiff and delay terms. At the moment, only a few low-order algorithms offer acceptabl...