This paper investigates the feedback stabilization of non-homogeneous delayed bilinear systems, evolving in Hilbert state space. More precisely, under observability like assumption, we prove the exponential and strong stability of the solution by using a bounded feedback control. The partial stabilization is discussed as well. The proof of the main results is based on the decomposition method. The decay estimates of the corresponding solution are obtained. Finally, some examples are presented.

In this paper, we deal with the numerical approximation of the coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term. Since the equation is a nonlinear equation, the Raviart-Thomas mixed finite element method is one of the most suitable techniques to obtain the approximated solution. In this paper, we will show that using the Raviart-Thomas method the optimal convergence order of the scheme can be achieved. To that end, we prove the necessary lemmas and the main theorem. Finally, the efficiency of the method is certified by numerical examples.

In this paper, we study a class of sequential fractional differential inequalities involving Caputo fractional derivatives with different orders. The nonexistence of nontrivial global solutions is investigated in a suitable space via the test function technique and some properties of fractional integrals. Our results are supported by numerical examples.

In this paper, we study the vaporization process of a polydisperse ensemble of liquid drops on the basis of a nonlinear set of balance and kinetics equations for the particle-radius distribution function and temperature in the gaseous phase. We found an exact parametric solution to this problem using a modified time variable and the Laplace integral transform method. The distribution function of vaporizing drops as well as its moments, the temperature dynamics in gas, and the unvaporized mass of drops are found. The initial particle-radius distribution shifts to smaller particle radii with increasing the vaporization time. As this takes place, the temperature difference between the drops and gas decreases with time. It is shown that the heat of vaporization and initial total number of particles in the system substantially influence the dynamics of a polydisperse ensemble of liquid drops.

In this paper, authors introduce the generalized Bessel-Maitland transform whose kernel is the generalized Bessel-Maitland function. New identities are obtained for special cases of the generalized Bessel-Maitland function. Using these relations, several identities are obtained for generalized Bessel-Maitland integral transform. It is shown that some special cases of them are related with the Laplace transform and the Hankel transform. Also, some examples are given as representations of the outcomes presented here.

The formulation and analysis of two operator Boundary-Domain Integral Equation systems for variable coefficient mixed BVP with in two dimensional domain is discussed. To analyse the two-operator approach, we applied one of its linear versions to the mixed (Dirichlet-Neumann) BVP for a linear second-order scalar elliptic variable-coefficient PDE and reduced it to four different BDIE systems. %The two-operator BDIE systems are nonstandard systems of equations containing integral operators defined on the domain under consideration and potential type and pseudo-differential operators defined on open sub-manifolds of the boundary. Using the results as in CMN09 andAM11, a rigorous analysis of the two-operator BDIE systems is given and it is shown that they are equivalent to the mixed BVP and thus are uniquely solvable, while the corresponding boundary domain integral operators are invertible in the appropriate Sobolev-Slobodetski (Bessel potential) spaces.

The paper deals with boundedness problems of  integral operators in weighted grand Bochner-Lebesgue spaces. We will treat both cases: when a weight function appears as a multiplier in the definition of the norm, or when it defines the absolute continuous measure of integration. Along with the diagonal case we deal with the off-diagonal case. To get the appropriate result for the Hardy-Littlewood maximal operator we rely on the reasonable bound of the sharp constant in the Buckley type theorem which is also derived in the paper.

A document by Cheima Khennaoui. Click on the document to view its contents.

As the COVID-19 continues to mutate, the number of infected people is increasing dramatically, and the vaccine is not enough to fight the mutated strain. In this paper, a SEIR-type fractional model with reinfection and vaccine inefficacy is proposed, which can successfully capture the mutated COVID-19 pandemic. The existence, uniqueness, boundedness and nonnegativeness of the fractional model are derived. Based on the basic reproduction number R 0 , locally stability and globally stability are analyzed. The sensitivity analysis evaluate the influence of each parameter on the R 0 and rank key epidemiological parameters. Finally, the necessary conditions for implementing fractional optimal control are obtained by Pontryagin's Maximum Principle, and the corresponding optimal solutions are derived for mitigation COVID-19 transmission. The numerical results show that humans will coexist with COVID-19 for a long time under the current control strategy. Furthermore, it is particularly important to develop new vaccines with higher protection rates.

The Dirichlet, Neumann and mixed boundary value problems for the linear second-order scalar elliptic differential equation with variable coefficient in a bounded three-dimensional domain are considered. The PDE right-hand side belongs to $H^{-1}(\Omega)$ or $\widetilde{H}^{-1}(\Omega),$ when neither classical nor canonical co-normal derivatives are well defined. Using the two-operator approach and appropriate parametrix (Levi function) each problem is reduced to different systems of boundary domain integral equations (BDIEs). Equivalence of the BDIEs to the original BVP, BDIE solvability, solution uniqueness/non-uniqueness, and as well as invertibility of the BDIE operators are analysed in appropriate Sobolev (Bessel potential) spaces. It is shown that the BDIE operators for the Neumann BVP are not invertible, and appropriate finite-dimensional perturbations are constructed leading to invertibility of the perturbed operators.

In this paper, we investigate the surface-dependent growth model in Euclidean 3-space. The surface-dependent model is developed to model the kinematics of surface growth for objects that can be generated by the curves on the surface, such as parasites and plants. This paper includes two main purposes for this model. The first one is to parametrize this model by using the quaternions and homothetic motions.Furthermore, we express the matrix representations of the surface-dependent growth model. The second one is to construct the surface-dependent growth model by using the growth velocity components related to the Darboux frame at each point of the generating curve. Moreover, to support the theory studied in the paper various illustrated examples are presented.

The purpose of this paper is to construct generating functions in terms of hypergeometric function and logarithm function for finite and infinite sums involving higher powers of inverse binomial coefficients. These generating functions provide a novel way of examining higher powers of inverse binomial coefficients from the perspective of these sums, assessing how several of these sums and these coefficients related to each other. A unique relation between the Euler-Frobenius polynomial and B-spline associated with exponential Euler spline is reported. Moreover, with the aid of derivative operator and functional equations for generating functions, many new computational formulas involving the special finite sums of higher powers of (inverse) binomial coefficients, the Bernoulli polynomials and numbers, Euler polynomials and numbers, the Stirling numbers, the harmonic numbers, and finite sums are derived. Moreover, A few recurrence relations containing these particular finite sums are given. Using these recurence relations, we give a solution of the problem which was given by Charalambides7, Exercise 30, p. 273. We give calculations algorithms for these finite sums. Applying these algorithms and Wolfram Mathematica 12.0, we give some plots and many values of these polynomials and finite sums.

We discuss the existence and nonexistence of a local and global-in-time solution to the fractional problem $$ ¥begin{cases} ¥partial_t^{¥alpha}u=¥Delta u+f(u) & x¥in¥Omega,¥ 01$ one has $|f(¥xi)-f(¥eta)|¥le C(1+|¥xi|+|¥eta|)^{p-1}|¥xi-¥eta|$ for all $¥xi, ¥eta¥in ¥R$. Particular attention is paid to the doubly critical case $(p,r)=(1+2/N,1)$.

In this study, the viscosity of MgO-Water nanofluid in a different volume fraction of nanoparticles, temperatures, and shear rates has been predicted by Artificial Neural Networks (ANNs) and surface methods. In the ANN method, an algorithm is proposed to select the best neuron number for the hidden layer. In the fitting method, a surface is proposed for each volume fraction of nanoparticles, and finally, the results of ANN and surface fitting method have been compared. It can be observed that, increasing the volume fraction from 0.07% to 1.25% at temperatures of 25, 30, 40, 50, and 60 °C resulted in about two-fold increase in viscosity. Also, the best network has 24 neurons in the hidden layer. It can be seen that for a network with 24 neurons in the hidden layer has the best overall correlation, and this coefficient is 0.999035. The mean absolute value of errors in ANN and fitting method are 0.0118 and 0.0206, respectively.

The substantial, tempered, and shifted fractional derivatives are introduced in a unified framework. Their properties are studied and, in the light of the strict sense criterion for derivative definitions, they are characterized and assessed. In the scope of the framework, new tempered linear sytems and transfer functions are introduced.

Since December 2019 that coronavirus pandemic (COVID-19) has hit the world, with over 13 million cases recorded, only a little above 4.67 percent of the cases have been recorded in the continent of Africa. The percentage of cases in Africa rose significantly from 2 percent in the month of May 2020 to above 4.67 percent by the end of July 15, 2020. This rapid increase in the percentage indicates a need to study the transmission, control strategy, and the dynamics of COVID-19 in Africa continent. In this study, a nonlinear mathematical model to investigate the impact of asymptomatic cases on the transmission dynamics of COVID-19 in Africa is proposed. The model is analyzed, the reproduction number is obtained, the local, as well as the global, asymptotic stability of the equilibria were established. We investigate the existence of backward bifurcation and we present the numerical simulations to verify our theoretical results.

We define multiplicative derivative and its properties on time scales. Then, we restate many concepts for multiplicative analysis such as derivative, Rolle's theorem, mean value theorem and increasing decreasing property on time scales. We aim to create important fields of study by carrying this most important issue of multiplicative analysis, which has applications in economics, finance and many other fields, to time scale calculus

In this paper, we construct the Riemann-Liouville fractional integral and differential operator of bicomplex order and illustrate some examples to calculate the fractional integration and differentiation of bicomplex order of some elementary functions. Also, we discuss some properties of these operators by proving analogues of the Leibniz and chain rules for these operators.