Article
Computer Science, Theory & Methods
Vu Ho, Van Hoa Ngo
Summary: This paper investigates a non-instantaneous impulsive value problem of interval differential equations using the Caputo-Katugampola fractional derivative concept. The main purposes are to study the existence and uniqueness of the solution, and to present the stability results of the problem. Examples are provided to illustrate the main results.
FUZZY SETS AND SYSTEMS
(2021)
Article
Mathematics, Interdisciplinary Applications
Assia Boudjerida, Djamila Seba
Summary: This paper discusses the approximate controllability of a class of non-instantaneous impulsive hybrid systems under Hilfer derivative, using a family of general fractional resolvent operators to obtain a proper form of the mild solution, and improving and extending important results through Laplace transform.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Multidisciplinary Sciences
Zainab Alsheekhhussain, Ahmed Gamal Ibrahim
Summary: This study investigated the controllability of a semilinear multi-valued differential equation with non-instantaneous impulses of order alpha, where the linear part is a strongly continuous cosine family without compactness. Unlike previous literature, no compactness conditions were assumed on the semi-group, the multi-valued function, or the inverse of the controllability operator.
Article
Mathematics, Applied
Abdelkader Moumen, Ammar Alsinai, Ramsha Shafqat, Nafisa A. Albasheir, Mohammed Alhagyan, Ameni Gargouri, Mohammed M. A. Almazah
Summary: In this study, the Hilfer derivative is utilized to analyze the approximate controllability of fractional stochastic evolution inclusions (FSEIs) with nonlocal conditions. By assuming that the corresponding linear system is approximately controllable, a novel set of adequate requirements for the approximate controllability of nonlinear FSEIs is obtained in meticulous detail. The results are achieved by employing the fixed-point theorem for multi-valued operators and fractional calculus. Finally, several instances are used to demonstrate the findings.
Article
Mathematics, Interdisciplinary Applications
Abdelkrim Salim, Mouffak Benchohra, John R. Graef, Jamal Eddine Lazreg
Summary: This manuscript proves the existence of solutions to a class of boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional derivatives, using Banach's contraction principle and Krasnosel'skii's fixed point theorem. An example is provided to illustrate the results.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Applied
Vipin Kumar, Muslim Malik, Amar Debbouche
Summary: This paper proves the existence, stability, and controllability of fractional damped differential systems with non-instantaneous impulses. The results are obtained using mathematical methods and illustrated with numerical examples.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
K. Sanjay, P. Balasubramaniam
Summary: This manuscript investigates the controllability of Hilfer fractional neutral differential inclusions with non-instantaneous impulse in Banach space using semi-group theory, fractional calculus, upper semi-continuous (u.s.c), multi-functions, and Monch fixed point theorem. Sufficient conditions are derived using the Hausdorff measure of non-compactness (MNC). Furthermore, the obtained result is illustrated through an example.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2022)
Article
Mathematics, Interdisciplinary Applications
Rajesh Dhayal, Muslim Malik
Summary: This work investigates a new class of fractional stochastic differential equations driven by the Rosenblatt process with non-instantaneous impulses. By utilizing the sectorial operator, fractional calculus, and Krasnoselskii's fixed point theorem, the approximate controllability results for the proposed system are studied. An illustrative example is provided to demonstrate the validity of the results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
M. Mallika Arjunan, Thabet Abdeljawad, V. Kavitha, Ali Yousef
Summary: This paper examines the existence of piecewise-continuous mild solution of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions (ABFVFIDI) with non-instantaneous impulses (NII) in Banach space. The main results are developed based on Martelli's fixed point theorem and rho-resolvent operators, with an example provided to support the validation of the theoretical results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Truong Vinh An, Ho Vu, Ngo Van Hoa
Summary: This study presents, for the first time, the result on finite-time stability (FTS) for fractional delay differential equations with non-instantaneous impulses (NI-FDDEs) involving the generalized Caputo fractional derivative. A sufficient condition for the FTS of NI-FDDEs is proposed based on an extensive estimation of the fractional integral inequality provided in this paper. Several examples are presented to illustrate the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Avadhesh Kumar, Ankit Kumar, Ramesh Kumar Vats, Parveen Kumar
Summary: This paper establishes the approximate controllability results for fractional neutral integro-differential inclusions with non-instantaneous impulse and infinite delay, providing sufficient conditions for the proposed control problem. The study utilizes tools such as the fixed point theorem for discontinuous multi-valued operators and the alpha-resolvent operator. The proposed results are finally demonstrated through an example.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2021)
Article
Mathematics, Applied
Said Abbas, Mouffak Benchohra, Juan J. Nieto
Summary: This paper discusses the existence of solutions for Caputo-Fabrizio fractional differential equations with instantaneous impulses, using Schauder's and Monch's fixed point theorems and the technique of the measure of noncompactness. Two illustrative examples are presented in the last section.
Article
Mathematics, Applied
Kottakkaran Sooppy Nisar, Kasthurisamy Jothimani, Chokkalingam Ravichandran, Dumitru Baleanu, Devendra Kumar
Summary: This study discusses the controllability of the nondense Hilfer neutral fractional derivative (HNFD) using Winch theorem and Banach contraction technique, and presents a numerical approximation method to handle different criteria of the results.
Article
Automation & Control Systems
Rajesh Dhayal, Muslim Malik, Syed Abbas
Summary: This paper focuses on a new class of non-instantaneous impulsive stochastic differential equations driven by mixed fractional Brownian motion in separable Hilbert spaces. By utilizing various theoretical methods, the existence and uniqueness of mild solutions for the system are ensured, the asymptotic behavior of mild solutions and controllability results are investigated, and the applicability of the results is demonstrated through an example.
INTERNATIONAL JOURNAL OF CONTROL
(2022)
Article
Computer Science, Artificial Intelligence
Hui Li, Yonggui Kao, Haibo Bao, Yangquan Chen
Summary: This paper discusses the complex-valued neural network based on CV parameters and variables, focusing on the fractional-order CVNN with linear impulses and fixed time delays. Criteria for uniform stability and existence and uniqueness of equilibrium solutions were derived using the sign function, Banach fixed point theorem, and two classes of activation functions. Three experimental simulations were presented to illustrate the correctness and effectiveness of the obtained results.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
