Article
Mathematics
Hamdy M. Ahmed, Maria Alessandra Ragusa
Summary: This paper studies Sobolev-type conformable fractional stochastic evolution inclusions with Clarke subdifferential and nonlocal conditions. By using fractional calculus, stochastic analysis, properties of Clarke subdifferential, and nonsmooth analysis, sufficient conditions for nonlocal controllability for the considered problem are established.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Hamdy M. Ahmed, Mahmoud M. El-Borai, Wagdy El-Sayed, Alaa Elbadrawi
Summary: This paper explores the null controllability for nonlocal stochastic differential inclusion with the Hilfer fractional derivative and Clarke subdifferential. The sufficient conditions for null controllability are established using the fixed-point approach, with proof of controllability for the corresponding linear system. The theoretical results are verified through an example.
FRACTAL AND FRACTIONAL
(2022)
Article
Operations Research & Management Science
Jing Li, Maojun Bin
Summary: This paper focuses on control systems described under certain conditions, and investigates the properties of the control constraints as well as the relaxation properties among the solution sets.
Article
Mathematics, Applied
C. Dineshkumar, R. Udhayakumar, V. Vijayakumar, Anurag Shukla, Kottakkaran Sooppy Nisar
Summary: In this paper, we investigate the approximate controllability of Sobolev-type fractional stochastic evolution hemivariational inequalities. By employing various methods, we establish the existence of mild solutions for the fractional stochastic evolution systems and provide a sufficient condition for the approximate controllability of the systems. Furthermore, our results are applicable to problems involving nonlocal conditions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Anjali Upadhyay, Surendra Kumar
Summary: This study investigates the existence and uniqueness of a new class of stochastic multi-term fractional differential inclusions involving the Rosenblatt process using the successive approximation approach, stochastic analysis methodology, and resolvent operators. Additionally, new sufficient conditions are provided for the exponential decay of the mild solution without Lipschitz conditions on non-linear terms. An example is also presented to confirm the obtained results.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Multidisciplinary
Tran Ngoc Thach, Devendra Kumar, Nguyen Hoang Luc, Nguyen Duc Phuong
Summary: The present paper investigates a nonlocal problem for semilinear fractional diffusion equations with Riemann-Liouville derivative. By applying Banach fixed point theorem and techniques on Mittag-Leffler functions, results on the existence, uniqueness, and regularity of mild solutions in suitable spaces are established. Additionally, the convergence of mild solutions as the parameter tends to zero is shown, and numerical examples are presented to illustrate the proposed method.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Engineering, Multidisciplinary
JinRong Wang, Ahmed G. Ibrahim, Donal O'Regan, Adel A. Elmandouh
Summary: This paper establishes the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order a, generated by a cosine family of bounded linear operators. It also demonstrates the compactness of the solution set, considering cases where the values of the multivalued function are convex and nonconvex. Examples are provided to illustrate the theory.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2021)
Article
Mathematics, Applied
Hong-Kun Xu, Vittorio Colao, Luigi Muglia
Summary: This study investigates the existence of mild solutions for a nonlocal semilinear evolution equation on an unbounded interval using an approximation solvability method, without assuming compactness on the evolution system and nonlinearity. The method is based on reducing the problem to a finite dimensional one through projections solved by a fixed point approach, including a compactness criterion on BC([0, +infinity), E). Continuation principle and weak topology are also utilized.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Jiangfeng Han, Changpin Li, Shengda Zeng
Summary: This paper studies a generalized fractional hemivariational inequality in infinite-dimensional spaces and delivers an existence result using the temporally semi-discrete scheme and the surjectivity result for multivalued pseudomonotone operator. As an illustrative application, a frictional contact model describing the quasi-static contact between a viscoelastic body and a solid foundation is proposed. The weak solvability of the mechanical system is obtained by using the abstract mathematical result presented in this paper.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Marius Ghergu, Yasuhito Miyamoto, Masamitsu Suzuki
Summary: We discuss the existence and nonexistence of local and global-in-time solutions to a fractional problem. The problem is a partial differential equation that satisfies certain conditions, with a particular focus on the doubly critical case.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Zuomao Yan
Summary: This paper investigates time optimal control for a class of non-instantaneous impulsive Clarke subdifferential type stochastic evolution inclusions in Hilbert spaces. By using measures of non-compactness and a fixed-point theorem with the properties of Clarke subdifferential, the existence of mild solutions is focused on, and the existence of time optimal control governed by stochastic control systems is also obtained. An example is provided to illustrate the effectiveness of the results.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Mathematics, Applied
Tiziana Cardinali, Elisa Continelli
Summary: In this paper, we investigate the controllability of a Cauchy problem governed by a nonlinear differential inclusion driven by a Sturm-Liouville type operator. By using a multivalued version of a recently proved theorem, we prove the existence of a local admissible pair for the considered control problem and the increased regularity for the solutions. The regularity obtained is the same as that recently tested for a different type of problem involving the Sturm-Liouville operator by Bonanno, Iannizzotto, and Marras.
RESULTS IN MATHEMATICS
(2023)
Article
Multidisciplinary Sciences
Sarra Guechi, Rajesh Dhayal, Amar Debbouche, Muslim Malik
Summary: This paper investigates a new class of phi-Hilfer fractional differential equations with impulses and nonlocal conditions. The existence and uniqueness of mild solutions for the proposed fractional system are obtained using fractional calculus, semigroup theory, and the fixed point theorem. The existence of optimal controls for the phi-Hilfer fractional control system is also discussed, with main results supported by an illustrative example.
Article
Engineering, Multidisciplinary
Sadam Hussain, Muhammad Sarwar, Gul Rahmat, Hassen Aydi, Manuel De La Sen
Summary: This work aims to study the existence and controllability of fractional evolution inclusions of Clarke's subdifferential type with nonlocal conditions in Hilbert spaces. By using fixed point techniques, fractional calculus, multivalued maps, cosine and sine function operators, the existence of mild solutions for the considered system is discussed. Furthermore, the controllability of the proposed system is investigated under suitable conditions. An illustrated example is presented.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Mathematics, Applied
Mohammed M. Matar, Esmail S. Abu Skhail, Jehad Alzabut
Summary: This paper investigates the existence and uniqueness of solutions for nonlinear fractional differential systems with order alpha is an element of(1,2], using the Banach and Schauder fixed point theorems. Two examples are provided to examine the theoretical findings.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
