Impulsive Nonlocal Neutral Integro-Differential Equations Controllability results on Time Scales

In this work, we studied the controllability results for neutral differential time-varying equation with impulses on time scales & extend these results into nonlocal controllability of neutral functional integro-differential time-varying equation with impulses on time scales. The solutions are obtained employing standard fixed point theorems

Existence and Stability Results of Nonlinear Fractional Differential Equations with Nonlinear Integral Boundary Condition on Time Scales

In this paper, we establish the existence and uniqueness of the solution to a nonlinear fractional differential equation with nonlinear integral boundary conditions on time scales.We used the fixed point theorems due to Banach, Schaefer’s, nonlinear alternative of Leray Schauder’s type and Krasnoselskii’s to establish these results. In addition, we study Ulam-Hyer’s (UH) type stability result. At the end, we present two examples to show the effectiveness of the obtained analytical results

Controllability of a semilinear neutral dynamic equation on time scales with impulses and nonlocal conditions

In this paper we consider a control system governed by a neutral differential equation on time scales with impulses and nonlocal conditions. We obtain conditions under which the system is approximately controllable, on one hand, and on the other hand, the exactly controllable is also proved. Concretely, first of all, we prove the existence of solutions. After that, we prove approximate controllability assuming that the associated linear system on time scales is exactly controllable, and applying a technique developed by Bashirov et al. [8, 9, 10] where we can avoid fixed point theorems. Next, assuming certain conditions on the nonlinear term, we can apply Banach Fixed Point Theorem to prove exact controllability. Finally, we propose an example to illustrate the applicability of our results.Publisher's Versio

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

Approximate controllability for some integrodifferential measure driven system with nonlocal conditions

In this work, we focus on a specific category of nonlocal integrodifferential equations. The development of a few new sufficient postulates that guarantee solvability and approxi- mative controllability is described here. We apply the theory of the resolvent operator in the sense of Grimmer, as well as the fixed point strategy and the theory of the Lebesgue-Stieljes integral, in the context of the space of regulated functions. In light of this, the prevalence of our findings is greater than that which is found in the literature. At last, and example is comprised that exhibits the significance of developed theory

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

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

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

Qualitative Theory of Switched Integro-differential Equations with Applications

Switched systems, which are a type of hybrid system, evolve according to a mixture of continuous/discrete dynamics and experience abrupt changes based on a switching rule. Many real-world phenomena found in branches of applied math, computer science, and engineering are naturally modelled by hybrid systems. The main focus of the present thesis is on hybrid impulsive systems with distributed delays (HISD). That is, studying the qualitative behaviour of switched integro-differential systems with impulses. Important applications of impulsive systems can be found in stabilizing control (e.g. using impulsive control in combination with switching control) and epidemiology (e.g. pulse vaccination control strategies), both of which are studied in this work. In order to ensure the models are well-posed, some fundamental theory is developed for systems with bounded or unbounded time-delays. Results on existence, uniqueness, and continuation of solutions are established. As solutions of HISD are generally not known explicitly, a stability analysis is performed by extending the current theoretical approaches in the switched systems literature (e.g. Halanay-like inequalities and Razumikhin-type conditions). Since a major field of research in hybrid systems theory involves applying hybrid control to problems, contributions are made by extending current results on stabilization by state-dependent switching and impulsive control for unstable systems of integro-differential equations. The analytic results found are applied to epidemic models with time-varying parameters (e.g. due to changes in host behaviour). In particular, we propose a switched model of Chikungunya disease and study its long-term behaviour in order to develop threshold conditions guaranteeing disease eradication. As a sequel to this, we look at the stability of a more general vector-borne disease model under various vaccination schemes. Epidemic models with general nonlinear incidence rates and age-dependent population mixing are also investigated. Throughout the thesis, computational methods are used to illustrate the theoretical results found

Nonlinear Modeling and Identification of Unsteady Aerodynamics at Stall

For an aircraft with delta wing shape, aerodynamics in stall angles-of-attack at both low and high-subsonic Mach conditions is known to be unsteady and nonlinear in nature. In these conditions, the longitudinal aerodynamic loads depend on the history of angle-ofattack and side-slip. The classical method of using damping or acceleration aerodynamic derivatives for modeling the unsteady variation of coefficients is unsuitable. Hence, two novel approaches for modeling aerodynamic loads in these conditions are proposed in this thesis. The unsteady effect in stall conditions at low Mach number is reflected in forced oscillation wind tunnel tests as dependence of longitudinal loads on amplitude and frequency of sinusoidal angle-of-attack input. The variations in longitudinal loads are nonlinear as their power spectrum contains super-harmonics of input frequency. The approaches presented in literature are equivalent when these are reduced to equivalent linear transfer function formulation, while their nonlinear adaptations are semi-empirical or adhoc. Hence, Volterra Variational Modeling (VVM) is proposed as a systematic approach to capture the nonlinear nature of unsteady variations. The VVM is derived from Volterra series as a set of parametric differential equations of the so-called kernel states. The kernel-states have special harmonic input response properties which are leveraged to develop a systematic methodology to capture the nonlinear unsteady variations in pitching moment coefficient. VVM is shown to inherently reproduce the nonlinear features of unsteady aerodynamic loads like amplitude dependence of nonlinear variations, different effective time-scale for pitch-up and pitchdown motions and same number of super-harmonics as seen in the experimental data. Hence, it offers several advantages compared to all the modeling approaches in literature. The VVM is a powerful approach due to following features: (i) Mathematically rigorous structure, (ii) Physical interpretations of parameters, (iii) it facilitates linear analysis of the flight modes (iv) simple identification methodology using forced oscillation wind tunnel test data (v) open to innovations in model structure and estimation technique. These concepts are demonstrated for the Generic Tailless Aircraft and F16XL aircraft using comprehensive sets of wind tunnel test data . The unsteady phenomena at high sub-sonic Mach number is called AbruptWing Stall, and novel model called ”Bifurcational Model of Aerodynamic Asymmetry” is proposed for modeling it. It shown to be a topologically rich structure which can model the static hysteresis and unsteady variations in rolling moment coefficient versus the side-slip angle, in order to reproduce the effects of Abrupt Wing Stall on flight dynamics