70 research outputs found
On the -regular mild solution for fractional abstract integro-differential equations
In this present paper, we first obtained some estimates involving parts of
-regular mild solutions of the fractional integro-differential
equation. In this sense, through these preliminary results, we investigate the
main results of this paper, i.e., the existence, regularity and continuous
dependence of -regular mild solutions for fractional abstract
integro-differential equations in Banach space.Comment: 20 page
Cauchy-Lipschitz theory for fractional multi-order dynamics -- State-transition matrices, Duhamel formulas and duality theorems
The aim of the present paper is to contribute to the development of the study
of Cauchy problems involving Riemann-Liouville and Caputo fractional
derivatives. Firstly existence-uniqueness results for solutions of non-linear
Cauchy problems with vector fractional multi-order are addressed. A qualitative
result about the behavior of local but non-global solutions is also provided.
Finally the major aim of this paper is to introduce notions of fractional
state-transition matrices and to derive fractional versions of the classical
Duhamel formula. We also prove duality theorems relying left state-transition
matrices with right state-transition matrices
Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects
We herein report a new class of impulsive fractional stochastic differential
systems driven by mixed fractional Brownian motions with infinite delay and
Hurst parameter . Using fixed point techniques, a
-resolvent family, and fractional calculus, we discuss the existence of a
piecewise continuous mild solution for the proposed system. Moreover, under
appropriate conditions, we investigate the approximate controllability of the
considered system. Finally, the main results are demonstrated with an
illustrative example.Comment: Please cite this paper as follows: Hakkar, N.; Dhayal, R.; Debbouche,
A.; Torres, D.F.M. Approximate Controllability of Delayed Fractional
Stochastic Differential Systems with Mixed Noise and Impulsive Effects.
Fractal Fract. 2023, 7, 104. https://doi.org/10.3390/fractalfract702010
Existence and continuous dependence of mild solutions for fractional abstract differential equations with infinite delay
In this paper, we prove the existence, uniqueness, and continuous dependence of the mild solutions for a class of fractional abstract differential equations with infinite delay. The results are obtained by using the Krasnoselskii's fixed point theorem and the theory of resolvent operators for integral equations
International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts
The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of
Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the
International Conference on Mathematical Analysis and Applications in Science and Engineering –
ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days).
Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering,
industry, and technology, to discuss the development of new mathematical models, theories, and
applications that contribute to the advancement of scientific knowledge and practice. Authors proposed
research in topics including partial and ordinary differential equations, integer and fractional order
equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization,
control, probability, computational mathematics, amongst others.
The conference was designed to maximize the involvement of all participants and will present the state-of-
the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio
A time-fractional mean field game
We consider a Mean Field Games model where the dynamics of the agents is
subdiffusive. According to the optimal control interpretation of the problem,
we get a system involving fractional time-derivatives for the
Hamilton-Jacobi-Bellman and the Fokker-Planck equations. We discuss separately
the well-posedness for each of the two equations and then we prove existence
and uniqueness of the solution to the Mean Field Games syste
Applied Mathematics and Fractional Calculus
In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia
Optimal control results for impulsive fractional delay integrodifferential equations of order 1 < r < 2 via sectorial operator
This research investigates the existence of nonlocal impulsive fractional integrodifferential equations of order 1 < r < 2 with infinite delay. To begin with, we discuss the existence of a mild solution for the fractional derivatives by using the sectorial operators, the nonlinear alternative of the Leray–Schauder fixed point theorem, mixed Volterra–Fredholm integrodifferential types, and impulsive systems. Furthermore, we develop the optimal control results for the given system. The application of our findings is demonstrated with the help of an example
A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order r∈(1,2) with impulses
In this article, we look into the important requirements for exact controllability of fractional impulsive differential systems of order 1<r<2. Definitions of mild solutions are given for fractional integrodifferential equations with impulses. In addition, applying fixed point methods, fractional derivatives, essential conditions, mixed Volterra-Fredholm integrodifferential type, for exact controllability of the solutions are produced. Lastly, a case study is supplied to show the illustration of the primary theorems
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