The Ulam stability of non-linear Volterra integro-dynamic equations on time scales

This manuscript presents the Ulam stability results of non-linear Volterra integro-dynamic equation and its adjoint equation on time scales. First, we obtain the Ulam stability of adjoint equation by using the integrating factor method. Then, the Ulam stability of the corresponding equation is proved by means of the property of the exponential function and related results that are proved in adjoint equation with the help of integrating factor method. At the end, an example is given that shows the validity of our main results

Stability of nonlinear impulsive higher order differential – fractional integral delay equations with nonlocal initial conditions

The aim of this paper is to investigate some types of stability such as generalized Hyers-Ulam- Rassias stability(G-H-U-R-stabile) and the relation with Hyers-Ulam(H-U-stabile) stable and Hyers-Ulam-Rassias stable (H-U-R-stabile) and generalized Hyers-Ulam stable (G-H-U- stable) to obtain which one guarantee to satisfy stability of equations included a nonlinear function some of them contains a delay time of solution and the other contain a vector of different order of  derivatives for the  solution to n-time  and vector of fractional order of integrals with different fractional orders and that was the for using a claculse of fractional calculus to satisfies the issue of this techniques. Moreover, the nonlocal initial   values for the proposal equation of nonlinear impulsive higher order differential – fractional integral delay time equations which are adding more interesting for nonlinear analytic object of nonlinear higher order integro – fractional order impulsive classes, and the impulsive difference of the equation has some necessary conditions to prove the results of solution to be stable with certain type has related with other types. The necessary and sufficient conditions which assumed on this nonlinear higher order integro-differential impulsive equation have been achieved the stability with interesting certain estimates obtain through the proving technique. Also the uniqueness of solution has been studied with same conditions was presented for stability and used for that issue a contraction fixed point theorem

Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions

In this paper we study existence and uniqueness of solutions for a coupled system consisting of fractional differential equations of Caputo type, subject to Riemann–Liouville fractional integral boundary conditions. The uniqueness of solutions is established by Banach contraction principle, while the existence of solutions is derived by Leray–Schauder’s alternative. We also study the Hyers–Ulam stability of mentioned system. At the end, examples are also presented which illustrate our results

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

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

Abstracts: Plenary Speakers

HI extensions of L ∞ spaces and spaces with very few operators Tuesday, July 30, HA4, We will present a general method of embedding Banach spaces with separable dual into L ∞ spaces admitting very few operators. In particular we will discuss the following two results. Theorem 1. (i) For every X with X * separable there exists a L ∞ space X such that X is isomorphic to a subspace X of X and X/ X is Hereditarily indecomposable satisfying the "scalar plus compact" property. (ii) If ℓ 1 is not isomorphic to a complemented subspace of X * then the aforementioned X satisfies the "scalar plus compact" property. The above yields that every separable reflexive space embeds into a L ∞ space satisfying the "scalar plus compact" property. ( HA4, It is well known that two non-isometric (and even non-isomorphic) Banach spaces can have isometric duals: the class of isometric preduals of l 1 provides classical examples. However, it frequently happens that a dual space has a unique isometric predual, as it is for instance the case for von Neumann algebras. We will provide simple topological tools which permit to show that weak-star closed spaces A of operators on a reflexive space X have unique isometric preduals as soon as weak-star approximation by compact operators is available in A. Some observations on approximation properties will also be mentioned. Pamela Gorkin (Bucknell University, USA) [email protected] Compositions of Blaschke products and three theorems of Frostman Thursday, August 1, HA4, 9:00-9:50 A recent Monthly article gave a very simple algorithm for determining when a polynomial is a composition of two (nontrivial) polynomials. A natural next step is to determine when finite Blaschke products are compositions of two Blaschke products, neither of which are automorphism of the disk. Well discuss several algorithms for determining when a finite Blaschke product can be a composition and then well discuss the current state of affairs for inner functions focusing, in particular, on three theorems of O. 2. M is in the closure of the set of injective factors on H with respect to the Effros-Marchal topology. 3. M admits an embedding i into the Ocneanu ultrapower N ω of the injective III 1 factor N with a normal faithful conditional expectation from N ω to M . 4. For every ε > 0, natural number n, and x 1 ,...,x n in natural cone P ♮ M in the standard form for M , there is a natural number k and a 1 , . . . , a n in . . , n, where tr k is the tracial state on M k (C). Magdalena Musat (University of Copenhagen, Denmark) [email protected] Factorizable completely positive maps and the Connes embedding problem Wednesday, July 31, HA4, The class of factorizable completely positive maps (originating in work of C. Anantharaman-Delaroche) has gained particular significance in quantum information theory in connection with the settling (in the negative) of the asymptotic quantum Birkhoff conjecture. More precisely, in joint work with Uffe Haagerup we proved earlier that every non-factorizable unital completely positive and trace-preserving map on M n (C), n ≥ 3, provides a counterexample for the conjecture. We will explain a recently established connection to the Connes embedding problem in terms of a newly formulated asymptotic property of factorizable maps. 3 Vern Paulsen (Houston University, USA) [email protected] Frames. Groups and the July 31, HA4, In this talk we will survey some of the new results on the Kadison-Singer problem and emphasize a few of the special cases that we believe are approachable. Volker Runde (University of Alberta, Canada) [email protected] Dual Banach algebras -an overview Sunday, August 4, HA4, A dual Banach algebra is a Banach algebra that is also a dual Banach space such that multiplication is separately weak* continuous. Von Neumann algebras are dual Banach algebras, but so are the measure algebras of locally compact groups. We discuss amenability properties for dual Banach algebras as well as their surprisingly intricate representation theory. Mikael Rørdam (University of Copenhagen, Denmark) [email protected] Supramenable groups and their actions on locally compact Hausdorff spaces Tuesday, July 30, HA4, It is well-known that a discrete group is amenable if and only if whenever it acts on a compact Hausdorff space, then there is an invariant probability measure. Similarly, a group is supramenable if and only if whenever it acts co-compactly on a locally compact Hausdorff space, then there is a nonzero invariant Radon measure. In this case the group admits a free minimal purely infinite (and often times also amenable) action on the locally compact (non-compact) Cantor set. We also discuss geometric characterizations of supramenable groups. The results are obtained by studying how groups act on their betacompactification. We shall discuss this action and its universal properties. This is joint work with J. Kellerhals and N. Monod, and in parts a work in progress with H. Matsui

Abstract book

Welcome at the International Conference on Differential and Difference Equations & Applications 2015. The main aim of this conference is to promote, encourage, cooperate, and bring together researchers in the fields of differential and difference equations. All areas of differential & difference equations will be represented with special emphasis on applications. It will be mathematically enriching and socially exciting event. List of registered participants consists of 169 persons from 45 countries. The five-day scientific program runs from May 18 (Monday) till May 22, 2015 (Friday). It consists of invited lectures (plenary lectures and invited lectures in sections) and contributed talks in the following areas: Ordinary differential equations, Partial differential equations, Numerical methods and applications, other topics