EQUADIFF 15

Equadiff 15 – Conference on Differential Equations and Their Applications – is an international conference in the world famous series Equadiff running since 70 years ago. This booklet contains conference materials related with the 15th Equadiff conference in the Czech and Slovak series, which was held in Brno in July 2022. It includes also a brief history of the East and West branches of Equadiff, abstracts of the plenary and invited talks, a detailed program of the conference, the list of participants, and portraits of four Czech and Slovak outstanding mathematicians

Existence of Solutions and Ulam Stability for Caputo Type Sequential Fractional Differential Equations of Order α ∈ (2,3)

We study initial value problems of sequential fractional differential equations and inclusions involving a Caputo type differential operator of the form: $\left(^{C}D_{a+}^{\alpha }+\lambda _{1}~^{C}D_{a+}^{\alpha -1}+\lambda _{2}~^{C}D_{a+}^{\alpha -2}\right),$ where $\alpha \in (2,3)$ and $\lambda _{i} (i=1, 2)$ are nonzero constants. Several existence and uniqueness results are accomplished by means of fixed point theorems. Sufficient conditions for Ulam stability of the given problem are also presented. Examples are constructed for the illustration of obtained results. Then we investigate the inclusions case of the problem at hand. An initial value problem for coupled sequential fractional differential equations is also discussed

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

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

Fractal fractional derivative on chemistry kinetics hires problem

In this work, we construct the fractional order model for chemical kinetics issues utilizing novel fractal operators such as fractal fractional by using generalized Mittag-Leffler Kernel. To overcome the constraints of the traditional Riemann-Liouville and Caputo fractional derivatives, a novel notion of fractional differentiation with non-local and non-singular kernels was recently presented. Many scientific conclusions are presented in the study, and these results are supported by effective numerical results. These findings are critical for solving the nonlinear models in chemical kinetics. These concepts are very important to use for real life problems like brine tank cascade, recycled brine tank cascade, pond pollution, home heating and biomass transfer problem. Many scientific results are presented in the paper also prove these results by effective numerical results. These results are very important for solving the nonlinear model in chemistry kinetics which will be helpful to understand the chemical reactions and its actual behavior; also the observation can be developed for future kinematic chemical reactions with the help of these results

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

New Challenges Arising in Engineering Problems with Fractional and Integer Order

Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem

New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus

This reprint focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems. It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention