In the paper, stability for fractional order differential equations is studied. Then the result obtained is applied to analyse the stability of equilibrium for the model of HIV.

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎the hybrid differential equations have a wide range of applications in science and engineering‎. ‎the hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎hybrid fuzzy differential equations (hfdes) is considered by ...

Spatial evolutionary games model individuals playing a game with their neighbors in a spatial domain and describe the time evolution of strategy profile of individuals over space. We derive integro-differential equations as deterministic approximations of strategy revision stochastic processes. These equations generalize the existing ordinary differential equations such as replicator dynamics a...

Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.

A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of differential equations in a Hilbert space. A feedback control ensuring strong stability of the equilibrium in the sense of Lyapunov is proposed. The proof of the ...

A theoretical framework for the stabilization of control systems defined by a class of nonlinear differential-algebraic equations is established. Assumptions are stated which guarantee that the nonlinear differential-algebraic equations can be described by a nonlinear control system defined on a smooth manifold. A procedure for obtaining a local state realization is developed. Conditions for lo...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

mathematical models can simulate the growth and proliferation of cells in the interaction with healthy cells, the immune system and measure the toxicity of drug and its effects on healthy tissue pay. one of the main goals of modeling the structure and growth of cancer cells is to find a control model suitable for administration among patients. in this study, a new mathematical model is designed...