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The article presents the statement of inverse problems of finding the right-hand side of the heat equation from an additional integral condition and justifies their Hadamard well-posedness in the class of regular solutions. The uniqueness of solutions of the problems is proved on the basis of integral identities. The solutions of the problems are constructed explicitly using separation of variables and the integral equation method. [ABSTRACT FROM AUTHOR]

The Levin‐Nohel integro‐differential equation is one of the famous equations in various fields of science and engineering. It was first studied by Volterra in connection with biological applications. This paper deals with the nonlinear neutral Levin‐Nohel integro‐differential equation with Caputo fractional derivative and variable delays. The Ulam‐Hyers‐Rassias stability, Ulam‐Hyers stability, semi‐Ulam‐Hyers‐Rassias stability are studied. The existence and uniqueness of solutions are established by using Krasnoselskii's fixed point theorem and contraction mapping principle. An illustrative example is also given and that is studied by the help of the Adomian decomposition method. [ABSTRACT FROM AUTHOR]

The paper proposes a method for solving the problem for a parabolic-hyperbolic equation of the third order in a rectangular domain, when the main part of equation contains a first-order operator. A criterion for the uniqueness of the solution is established. When justifying the uniform convergence of the Fourier series, the problem of small denominators arises. In this regard, estimates of small denominators about the distance from zero with the corresponding asymptotics are established. These estimates made it possible to prove the convergence of the series in the class of regular solutions of this equation. Estimates on the stability of the solution from given boundary functions are proved. [ABSTRACT FROM AUTHOR]

We discuss a few variations of the SEIRS epidemic model. How basic dynamical properties of the models can be derived by using some tools of the computer algebra system Mathematica is shown, and how invariant surfaces of the system can be found by using computer algebra system Singular is explained. Some numerical simulations are presented as well. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total population into the susceptible population S ( t ) $\mathcal{S}(t)$ , the vaccinated population V ( t ) $\mathcal{V}(t)$ , the infected population I ( t ) $\mathcal{I}(t)$ , the recovered population R ( t ) $\mathcal{R}(t)$ , and the death class D ( t ) $\mathcal{D}(t)$ . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii’s fixed point theorem, Schauder’s fixed point theorem, the Banach contraction principle, and Ulam–Hyers stability theorem.

In this paper, we consider a mathematical model of a coronavirus disease involving the Caputo–Fabrizio fractional derivative by dividing the total population into the susceptible population S (t) , the vaccinated population V (t) , the infected population I (t) , the recovered population R (t) , and the death class D (t) . A core goal of this study is the analysis of the solution of a proposed mathematical model involving nonlinear systems of Caputo–Fabrizio fractional differential equations. With the help of Lipschitz hypotheses, we have built sufficient conditions and inequalities to analyze the solutions to the model. Eventually, we analyze the solution for the formed mathematical model by employing Krasnoselskii's fixed point theorem, Schauder's fixed point theorem, the Banach contraction principle, and Ulam–Hyers stability theorem. [ABSTRACT FROM AUTHOR]

This paper deals with a fractional boundary value problem involving variable delays. Sufficient conditions for the existence of a unique solution are investigated. Moreover the stability of the unique solution is discussed. A numerical example that emphasizes the importance of the results obtained in this article is also included. [ABSTRACT FROM AUTHOR]

In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal–fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange’s interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study.

We study the stability and the solvability of a family of problems −(ϕ(x′))′=g(t,x,x′,u)+f* with Dirichlet boundary conditions, where ϕ, u, f* are allowed to vary as well. Applications for boundary value problems involving the p-Laplacian operator are highlighted.

The paper contains a discussion on solutions to symmetric type of fuzzy stochastic differential equations. The symmetric equations under study have drift and diffusion terms symmetrically on both sides of equations. We claim that such symmetric equations have unique solutions in the case that equations’ coefficients satisfy a certain generalized Lipschitz condition. To show this, we prove that an approximation sequence converges to the solution. Then, a study on stability of solution is given. Some inferences for symmetric set-valued stochastic differential equations end the paper.

The recent work on the solvability of the boundary value problem for the nonlinear analogue of the Boussinesq equation has been further extended to focus on the characteristics of the solution. Since this type of equation does not have a known analytical solution for arbitrary boundary conditions, the problem has been solved numerically. The stability of the solution and the effect of the input function on the stability have been investigated from the physics point of view. For the special case of a discontinuous function at the right hand side of the equation, the solution has been analyzed around the discontinuity points. [ABSTRACT FROM AUTHOR]

The finite-dimensional problem of the best approximation (in the Hausdorff metric) of a convex body by a ball of arbitrary norm with a fixed radius is considered. The stability and sensitivity of the solution to errors in specifying the convex body to be approximated and the unit ball of the used norm are analyzed. It is shown that the solution of the problem is stable with respect to the functional and, if the solution is unique, the center of the best approximation ball is stable as well. The sensitivity of the solution to the error with respect to the functional is estimated (regardless of the radius of the ball). A sensitivity estimate for the center of the best approximation ball is obtained under the additional assumption that the estimated body and the ball of the used norm are strongly convex. This estimate is related to the range of radii of the approximating ball. [ABSTRACT FROM AUTHOR]

The inverse problem of reconstructing the absorption coefficient (from L) in the multidi-mensional heat equation under an additional integral observation condition is studied. It is assumed that the minor coefficients belong to the Lebesgue space. For the solution to the inverse problem, sufficient conditions for existence, uniqueness, and stability to perturbations of input data are established. These conditions are formulated in the form of easy-to-check inequalities. [ABSTRACT FROM AUTHOR]

We show the existence of periodic and symmetric solutions of parametric weakly nonlinear ODE possessing time-reversal symmetries. Local asymptotic behaviours of these solutions are established aswell. Concrete examples are presented to illustrate the general theory. [ABSTRACT FROM AUTHOR]

We show the existence of unique periodic and symmetric solutions of weakly nonlinear ordinary differential equations. Conditions of stability and hyperbolicity of these solutions are established as well. Concrete examples are presented to show advantages of our method to the classical averaging theory. [ABSTRACT FROM AUTHOR]

We show the existence of periodic and symmetric solutions of weakly nonlinear ordinary differential equations at resonance. Asymptotic properties of these solutions are established as well. Concrete examples are presented to show advantages of our method to the classical averaging theory. [ABSTRACT FROM AUTHOR]

We study the stability and the solvability of a family of problems − (ϕ (x ′)) ′ = g (t , x , x ′ , u) + f * with Dirichlet boundary conditions, where ϕ , u, f * are allowed to vary as well. Applications for boundary value problems involving the p-Laplacian operator are highlighted. [ABSTRACT FROM AUTHOR]

The paper contains a discussion on solutions to symmetric type of fuzzy stochastic differential equations. The symmetric equations under study have drift and diffusion terms symmetrically on both sides of equations. We claim that such symmetric equations have unique solutions in the case that equations' coefficients satisfy a certain generalized Lipschitz condition. To show this, we prove that an approximation sequence converges to the solution. Then, a study on stability of solution is given. Some inferences for symmetric set-valued stochastic differential equations end the paper. [ABSTRACT FROM AUTHOR]