1 Methods for the solution of the parameter estimation problem in ordinary differential equations fall into two categories (a) the simultaneous method in which the objective function (for example the sum of squares of residuals) is minimised subject to the differential system as imposed constraints, and (b) the embedding method in which auxiliary conditions are adjoined to take up the extra deg...

The compact Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. It is further developed to be more flexible in solving the Optimal Control Problems (OCPs), by relaxing the definite conditions from a feasible solution to an arbitrary one for the derived Evolution Partial Differential Eq...

The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within its frame, the third evolution equation is developed. This equation only solves the control variables along the variation time to get the optimal solution, and...

A deterministic mathematical model for the transmission dynamics of Influenza is studied. Although the equilibria of the model could not be expressed in closed form, their existence and threshold conditions for their stability are theoretically investigated. It is shown that the diseasefree equilibrium is locally–asymptotically stable if the basic reproductive number R0 < 1 (thus, Influenza can...

The Variation Evolving Method (VEM), which seeks the optimal solutions with the variation evolution principle, is further developed to be more flexible in solving the Optimal Control Problems (OCPs) with terminal constraint. With the first-order stable dynamics to eliminate the infeasibilities, the Modified Evolution Partial Differential Equation (MEPDE) that is valid in the infeasible solution...

The growth of colorectal cancer tumors and their reactions to chemo-immunotherapeutic treatment with monoclonal antibodies (mAb) are discussed in this paper using a system fractional order differential equations (FDEs). mAb medications still at the research stage; however, takes into account mAbs that already use. major goal is demonstrate effectiveness medication Cetuximab significance IL-2 le...

and Applied Analysis 3 The purpose of this paper is to improve and extend the above mentioned results. We will delete the Lipschitz condition 1.5 for impulsive function Ik and the restriction condition 1.6 and improve condition 1.4 for nonlinear term f . Our main results are as follows. Theorem 1.1. Let E be an ordered Banach space, whose positive cone P is normal, A : D A ⊂ E → E be a closed l...

In this paper, we present an accurate numerical approach based on the reproducing kernel method (RKM) for solving second-order fuzzy initial value problems (FIVP) with symmetry coefficients such as symmetric triangles and trapezoids. Finding exact solution of FIVP is not easy task since definition will produce a complicated optimization problem. To overcome difficulty, developed to solve type p...

New properties of the first‐order Riemann–Liouville fractional integrals are proved and derivatives for equivalence class functions in analyzed. Solutions, normal solutions, generalized solutions initial value problems (IVPs) nonlinear differential equations (FDEs) with fraction introduced. The equivalences between FDEs corresponding (Volterra) integral established based on solutions. results e...