Search

Abstract: We study the boundedness of the solutions to a non-autonomous and non-linear differential equation of second order with two constant deviating arguments. We give two examples to illustrate the main results. By this work, we extend some boundedness results obtained for a differential equation with a constant deviating argument in the literature to the boundedness of the solutions of a differential equation with two constant deviating arguments. [Copyright &y& Elsevier]

A non-linear system of Volterra integro-fractional delay differential equations with Caputo fractional derivatives is considered. New sufficient conditions for uniform stability, asymptotic stability, and Mittag-Leffler stability of the zero solution of the unperturbed system, and the boundedness of all solutions of the perturbed system, are presented. The technique of proof involves the Razumikhin method with an appropriate Lyapunov function. For illustrative purposes, two examples are provided. • A non-linear system of Volterra integro-fractional delay differential equations with Caputo fractional derivatives is considered. • New sufficient conditions for uniform stability, asymptotic stability, and Mittag-Leffler stability of the zero solution of the unperturbed system, and the boundedness of all solutions of the perturbed system, are presented. • The technique of proof involves the Razumikhin method with an appropriate Lyapunov function. • For illustrative purposes, two examples are provided. [ABSTRACT FROM AUTHOR]

Abstract: We establish some sufficient conditions which guarantee asymptotic stability of the null solution and boundedness of all the solutions of the following nonlinear differential equation of third order with the variable delay, r(t) when p(t, x(t), x′(t), x(t−r(t)), x′(t−r(t)), x′′(t))=0 and ≠0, respectively. By defining an appropriate Lyapunov functional, we prove two new theorems on the stability and boundedness of the solutions of the above equation. We also give an example to illustrate the theoretical analysis in this work. Our results improve a stability result in the literature, which was obtained for nonlinear differential equations of third order without delay, to the above differential equation with delay for stability and boundedness of the solutions. [Copyright &y& Elsevier]

Abstract: A theorem is presented that contains some sufficient conditions to ensure bound of solutions to a third-order nonlinear delay differential equation. It is shown that this theorem improves the result of Ponzo [On the stability of certain nonlinear differential equations, IEEE Trans. Automatic Control AC-10 (1965) 470–472] to the bound of solutions for the equation considered. [Copyright &y& Elsevier]

Abstract: In this paper, we investigated the differential equationin two cases; (a) and (b) . For the case (a), the stability of the solution and the uniform boundedness of all solutions of this equation are investigated; in the case (b) the boundedness of all solutions of the same equation is discussed. [Copyright &y& Elsevier]

Abstract: In this paper, the second order non-linear differential equation is considered, and Lyapunov''s second method is used to show that uniform boundedness and convergence to zero of all solutions of this equation together with their derivatives of the first order. [Copyright &y& Elsevier]

The nonlinear Schrodinger equation (NLSE) with Atangana's conformable fractional derivative (ACFD) is an equation that describes how the quantum state of a physical system changes in time. This present study examines the exact soliton results (ESRs) and analyze their bifurcations and phase plane (PP) of the NLSE with ACFD through the modified (G ′/ G)-expansion scheme (MG ′/ GES). Firstly, ACFD and its properties are included and then by MG ′/ GES , the exact soliton results and analyze their bifurcations and phase plane of NLSE, displayed with the ACFD, are classified. These obtained ESRs include periodic wave pulse, bright-dark periodic wave pulse, multiple bright-dark soliton pulse, and so many types. We provide 2-D, 3-D and contour diagrams, Hamiltonian function (HF) for phase plane dynamics analysis and bifurcation analysis diagrams to examine the nonlinear effects and the impact of fractional and time parameters on these obtained ESRs. The obtained ESRs illustration the novelty and prominence of the dynamical construction and promulgation performance of the resultant equation and also have practical effects for real world problems. The ESRs obtained with MG ′/ GES show that this scheme is very humble, well-organized and can be implemented to other the NLSE with ACFD. • Exact soliton solutions of the nonlinear Schrodinger equation with Atangana's conformable are studied. • Parametric effects are studied and characterized with 2-D, 3-D and contour plots. • Hamiltonian functions of the system are derived, and phase portrait is analyzed briefly. • Various categories of novel ESRs were achieved which enclosed very nearly entirely categories of solitary waves. [ABSTRACT FROM AUTHOR]

The main goal of the current research is to study and explore dynamic behavior of tuberculosis by using fractional mathematical model. In this study, recently introduced fractional operator (FO) having ML non-singular kernel was used. Fixed point theory is utilized to explore the unique and existing problems in suitable model. Numerical outcomes are discovered for the verification of arbitrary fractional order derivative. These numerical outcomes are discovered from mathematical and biological perspectives by using the model parameters values. Graphical simulation shows the comparison between Fractional Caputo (Fr. Cap) method and AB Caputo (AB Cap) predictor corrector method for different fraction order. The present study suggested that AB Cap is much better than Fr. Cap. • Fractional-mathematical model was used to explore the optimal control of the tuberculosis. • Fractional operator having Mittag-Leffler (ML) nonsingular kernel was used. • Fixed point method was used. • ABC predictor corrector and Fractional Caputo methods were compared for different fractional order. [ABSTRACT FROM AUTHOR]

• In this article, the non-integer equations of the coupled mass-spring system with Atangana Baleanu fractional derivatives is considered. • The physical entities of the structure are well-preserved by presenting an supplementary stricture χ. • A nonlinear model with damping factor is considered. • The existence and uniqueness problem to related model are scanned by fixed point principle. • Our consequences spectacle that the mechanical components reveal viscoelastic behaviors generating temporal fractality at diverse scales and exhibit the existence of material heterogeneities in the mechanical modules. • The comparison Jajarmi predictor corrector and Caputo methods is also given. In this article, the non-integer equations of the coupled mass-spring system with Atangana Baleanu fractional derivatives is offered. The physical entities of the structure are well-preserved by presenting an supplementary stricture χ. A nonlinear model with damping factor is considered. The existence and uniqueness problem to related model are scanned by fixed point principle. Our consequences spectacle that the mechanical components reveal viscoelastic behaviors generating temporal fractality at diverse scales and exhibit the existence of material heterogeneities in the mechanical modules. The comparison Jajarmi predictor corrector and Caputo methods is also given. [ABSTRACT FROM AUTHOR]