2,075 Results Found

In this paper, we investigate infinite interval problems for the fractional evolution equations with Hilfer fractional derivative. By using the generalized Ascoli–Arzelà theorem and some new techniques, we prove the existence of mild sol...

This paper is devoted to studying the existence and uniqueness of mild solutions for semilinear fractional evolution equations with the Hilfer–Katugampola fractional derivative and under the nonlocal multi-point condition. The analysis is based...

In this paper, we investigate the existence and uniqueness of mild solutions for non-autonomous fractional evolution equations (NFEEs) using the technique of non-compactness measure, focusing on scenarios where the semigroup is non-compact. Furthermo...

This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order $\alpha \in (1,2)$ . The main tools of our study include the concepts of...

Symmetry in systems arises as a result of natural design and provides a pivotal mechanism for crucial system properties. In the field of control theory, scattered research has been carried out concerning the control of group-theoretic symmetric syste...

In this paper, by utilizing the resolvent operator theory, the stochastic analysis method and Picard type iterative technique, we first investigate the existence as well as the uniqueness of mild solutions for a class of $\alpha \in (1,2)$...

In the scale of abstract Banach spaces, the existence as well as the controllability are considered for a class of evolution systems involving conformable fractional derivatives. Under essential conditions on nonlinearity, among other conditions, exi...

In this paper, we investigate the controllability of a class of impulsive $\psi$-Caputo fractional evolution equations of Sobolev type in Banach spaces. Sufficient conditions are presented by two new characteristic solution operators, fractional calcu...

In this paper, we mainly focus on the the existence of Hilfer fractional evolution inclusions with almost sectorial operators. For two cases in which the almost sector operators are compact and noncompact, we obtain existence criteria for mild soluti...

This paper presents a variational method for studying approximate controllability and infinite-dimensional exact controllability (finite-approximate controllability) for Riemann–Liouville fractional linear/semilinear evolution equations in Hilbert sp...

In this study, we investigate the existence of mild solutions for a class of Hilfer fractional stochastic evolution equations with order $\mu \in (1,2)$ and type $\nu \in [0,1]$. We prove the existence of mild solutions of Hilfer fractional stochasti...

This paper investigates the controllability of Hilfer fractional stochastic evolution equations (HFSEEs). Initially, we obtain a conclusion regarding the approximate controllability of HFSEEs by employing the Tikhonov-type regularization method and S...

This article focuses on deriving the averaging principle for Hilfer fractional stochastic evolution equations (HFSEEs) driven by Lévy noise. We show that the solutions of the averaged equations converge to the corresponding solutions of the or...

This work addresses the Ulam–Hyers stability of mild solutions of fractional noninstantaneous evolution nonlinear equations subject to noninstantaneous impulses in the Banach space through an approach based on the measure of noncompactness. Mil...

The purpose of this paper is to investigate the existence of attractive solutions for a Cauchy problem of fractional evolution equations with Hilfer fractional derivative, which is a generalization of both the Riemann–Liuoville and Caputo fract...

This paper concerns with the existence and uniqueness of fuzzy fractional evolution equation with uncertainty involves function of form ${}^c{D}^{\alpha }x\left(t\right)=f(t,x\left(t\right),D^{\beta }x\left(t\right)),I^{\alpha }x\left(0\right)=x_0,x^{\prime }\left(0\right)=x_1,$ where $1<\alpha <2,0<\beta <1$. Afte...

We investigate a class of fractional neutral evolution equations on Banach spaces involving Caputo derivatives. Main results establish conditions for the controllability of the fractional-order system and conditions for existence of a solution to an...

In this paper, we obtain new sufficient conditions of the existence of mild solutions for Hilfer fractional evolution equations in the cases that the semigroup associated with an almost sectorial operator is compact as well as noncompact. Our results...

The goal of this paper is to investigate the existence and uniqueness of pseudo $\mathcal{S}$-asymptotically periodic mild solutions for a class of neutral fractional evolution equations with finite delay. We essentially use the fractional powers of closed linea...

We look at estimates for the Green’s function of time-fractional evolution equations of the form $D_{0+\ast }^{\nu }u=Lu$ , where $D_{0+\ast }^{\nu }$ is a Caputo-type time-fractional derivative, depending on a Lév...

In this paper, we investigate a fuzzy Hilfer fractional evolution equation of type $0<\beta <1$ and order $1<\alpha <2$ subject to nonlocal conditions. Using the infinitesimal generator of a strongly continuous cosine family, we define a mild...

This paper investigates the existence and approximate controllability of Riemann–Liouville fractional evolution systems of Sobolev-type in abstract spaces. At first, a group of sufficient conditions is established for the existence of mild solu...

This paper examines a range of results that can be derived from Einstein’s evolution equation focusing on the effect of introducing a Lévy distribution into the evolution equation. In this context, we examine the derivation (derived excl...

In this paper, we study the nonexistence of global weak solutions to higher-order time-fractional evolution inequalities with subcritical degeneracy. Using the test function method and some integral estimates, we establish sufficient conditions depen...

In this paper, we study the stability for abstract coupled second-order evolution equations with one fractional infinite memory. By the frequency domain method, we show that the stability of the system depends on ${\displaystyle \frac{\mu }{\varrho }},$${\displaystyle \frac{a}{J}},$ and the order $\theta$...

In the present article, we establish conditions for the asymptotic periodicity of bounded mild solutions in two distinct cases of evolution equations. The first class involves non-densely defined operators, while the second class incorporates densely...

In this paper, we consider a weakly system of fractional $\theta$-evolution equations. Using the fixed-point theorem, a global-in-time existence of small data solutions to the Cauchy problem is proved for one single equation. Using these results, we p...

In this paper, we concentrate on a control system with a non-local condition that is governed by a Hilfer fractional neutral stochastic evolution hemivariational inequality (HFNSEHVI). By using concepts of the generalized Clarke sub-differential and...

The existence of mild solutions and the approximate controllability for a class of Sobolev-type $\psi$-Caputo fractional stochastic evolution equations (SCFSEEs) subject to nonlocal conditions and Poisson jumps are investigated in this paper. First, t...

This article concentrates on a control system with a nonlocal condition that is driven by neutral stochastic evolution hemivariational inequalities (HVIs) of Sobolev-type Hilfer fractional (HF). In order to illustrate the necessary requirements for t...

Under a new generalized definition of exact controllability we introduced and with a appropriately constructed time delay term in a special complete space to overcome the delay-induced-difficulty, we establish the sufficient conditions of the exact c...

In this paper, by using the cosine family theory, measure of non-compactness, the Mönch fixed point theorem and the method of estimate step by step, we establish the existence theorems of mild solutions for fractional impulsive integro-different...

This study presents a differential evolution (DE)-based optimization approach for fractional-order convolutional neural networks (FOCNNs) aimed at enhancing the accuracy of groove classification in music. Groove, an essential element in music percept...

Understanding the anisotropic mechanical behavior and pore–fracture structure (PFS) evolution of bedded coal under mining disturbance is critical for gas extraction and hazard prevention in deep coal mining. This study employed low-field nuclea...

The goal of this dissertation is to explore a system of fractional evolution equations with infinitesimal generator operators and an infinite time delay with non-local conditions. It turns out that there are two ways to regulate the solution. To demo...

Developing mathematical models of fractional order for physical phenomena and constructing numerical solutions for these models are crucial issues in mathematics, physics, and engineering. Higher order temporal fractional evolution problems (EPs) wit...

The study of small data Sobolev solutions to the Cauchy problem for weakly coupled systems of semi-linear fractional $\sigma –$evolution equations with different power nonlinearities is of interest to us in this research. These solutions must exi...

The purpose of this work is to investigate the controllability of non-instantaneous impulsive (NII) Hilfer fractional (HF) neutral stochastic evolution equations with a non-dense domain. We construct a new set of adequate assumptions for the existenc...

The topological properties of vector optical fields are traditionally considered strictly conserved during continuous deformations and linear propagation. However, while structured light has been extended into nonlinear regimes, previous studies have...

In this research article, we investigate a three-dimensional dynamical system governed by fractal-fractional-order evolution differential equations subject to terminal boundary conditions. We derive existence and uniqueness results using Schaefer&rsq...

In this paper, an effective numerical approach that combines the fast L1 formula and barycentric Lagrange interpolation is proposed for solving a kind of time-fractional evolution equations. This type of equation contains a nonlocal term involving th...

In this paper, based on the Schauder fixed point theorem, the (generalized) Darbo fixed point theorem, and the (generalized) Banach contraction mapping principle, we study the mixed-type fractional impulse evolution equation with non-local and delay...

We study in this paper the long-term existence of solutions to the system of weakly coupled equations with fractional evolution and various nonlinearities. Our objective is to determine the connection between the regularity assumptions on the initial...

This article is mainly concerned with the approximate controllability for some semi-linear fractional integro-differential impulsive evolution equations of order $1<\alpha <2$ with delay in Banach spaces. Firstly, we study the existence of the $PC$...

This paper presents a novel framework for modeling nonlinear fractional evolution control systems. This framework utilizes a power non-local fractional derivative (PFD), which is a generalized fractional derivative that unifies several well-known der...

An adaptive-uniform-experimental-design-based fractional particle swarm optimizer (AUFPSO) with non-linear time-varying evolution (NTE) is proposed. A particle swarm optimizer (PSO) is an excellent evolutionary algorithm due to its simple structure a...

We study the exact partial controllability of a semilinear stochastic fractional evolution equation of Caputo order $\alpha \in (1,2)$ in a separable Hilbert space, subject to a genuine state-dependent delay $y(t-\rho (t,y_t))$, impulsive effects,...

We establish a class of degenerate fractional differential equations involving delay arguments in Banach spaces. The system endowed by a given background and the generalized Showalter–Sidorov conditions which are natural for degenerate type equ...

This paper initiates a study on the existence and approximate controllability for a type of non-instantaneous impulsive stochastic evolution equation (ISEE) excited by fractional Brownian motion (fBm) with Hurst index $0<H<1/2$. First, to overcom...

In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in the Laurent...