Solvability of coupled systems of generalized Hammerstein-type integral equations in the real line

In this work, we consider a generalized coupled system of integral equations of Hammerstein-type with, eventually, discontinuous nonlinearities. The main existence tool is Schauder’s fixed point theorem in the space of bounded and continuous functions with bounded and continuous derivatives on R, combined with the equiconvergence at ±∞ to recover the compactness of the correspondent operators. To the best of our knowledge, it is the first time where coupled Hammerstein-type integral equations in real line are considered with nonlinearities depending on several derivatives of both variables and, moreover, the derivatives can be of different order on each variable and each equation. On the other hand, we emphasize that the kernel functions can change sign and their derivatives in order to the first variable may be discontinuous. The last section contains an application to a model to study the deflection of a coupled system of infinite beams

Nonlinear Differential Equations on Bounded and Unbounded Domains

Differential equations represent one of the strongest connections between Mathematics and real life. This is due to the fact that almost all the physical phenomena, as well as many other in economy, biology or chemistry, are modelled by differential equations. This Thesis includes a detailed study of nonlinear differential equations, both on bounded and unbounded domains. In particular, we analyze the qualitative properties of the solutions of nonlinear differential equations, focusing on the study of constant sign solutions on the whole domain of definition or, at least, on some subset of it. The main technique is based on the construction of an abstract formulation included into functional analysis, in which the solutions of the differential equations coincide with the fixed points of certain operators

Book of Abstracts: International Workshop on Mathematics and Physical Sciences

This book-proceeding comprises the results of various comprehensive Mathematical and Physical Sciences-based studies accepted for presentation and discussion during the 1st Mathematical and Physical Sciences International Workshop in Évora, in 2023 (Mat- Phys23). The MatPhys23, organized under the auspices of University of Évora throughout the CIMA - Research Center in Mathematics and Applications, the ICT - Institute of Earth Sciences and the NOVA-LINCS - NOVA Laboratory for Informatics and Computer Science (Évora branch). This Workshop brought together many well-known mathematicians, physicists and engineers from University of Beira Interior (UBI, Portugal), University of Cabo Verde (UCV, Cabo Verde), Montclair State University (MSU, NJ, USA) and University of Évora (UÉ, Portugal). This book-proceeding volume involves 24 abstracts on the latest trending and significant challenges in mathematics and physical sciences. The works presented focus on the following areas: statistical and mathematical methods that are relevant to biology, medical and biomedical sciences, computer science, economics, social sciences, music, environmental sciences, climatology, engineering, industry, fluid mechanics and their applications, numerical simulations in various physical, geophysical, chemical, biological and engineering applications. In addition to the usual scientific interaction between participants, this meeting has the presence of PhD students, which we consider relevant. Considering the original contents, aims, and methodologies of all these valuable studies, it is believed that the topical outputs are of interest to all researchers, practitioners, and students and would mainly provide new scientific insights and knowledge for geoscientists and engineers.CIMA-Centro de Investigação em Matemática e Aplicações; ICT-Instituto de Ciências da Terra; NOVALINC

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe

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

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

Stationary Distribution of Random Motion with Delay in Reflecting Boundaries

In this paper we study a continuous time random walk in the line with two boundaries [a,b], a < b. The particle can move in any of two directions with different velocities v1 and v2. We consider a special type of boundary which can trap the particle for a random time. We found closed-form expressions for the stationary distribution of the position of the particle not only for the alternating Markov process but also for a broad class of semi-Markov processes

Fractional Differential Equations, Inclusions and Inequalities with Applications

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering