In this paper, using the concept of horizontal membership functions, a new definition fuzzy derivative called granular is proposed based on difference. Moreover, integral defined, and its relation with given. A metric-granular metric-on space type-1 numbers, continuous functions are also presented. Restrictions associated to previous approaches-Hukuhara differentiability, strongly generalized Hukuhara Zadeh's extension principle, differential inclusions-dealing equations (FDEs) expressed. It...

Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis which can be controlled by vaccination as well treatment. Initially consider constant controls for both and case, determining basic reproduction number, existence stability disease-free endemic steady-state solutions model. Next, take time formulate appropriate optimal control problem obtain strategy to minimize number infectious humans associated costs. Finally at end...

Abstract This paper presents a novel extended modal series method for solving the infinite horizon optimal control problem of nonlinear interconnected large‐scale dynamic systems. In this method, two‐point boundary value (TPBVP), derived from Pontryagin's maximum principle, is transformed into sequence linear time‐invariant TPBVPs. Solving latter problems in recursive manner provides law and trajectory form uniformly convergent series. Moreover, special cases, proposed procedure facilitates...

The present study proposes a fuzzy mathematical model of HIV infection consisting linear differential equations (FDEs) system describing the ambiguous immune cells level and viral load which are due to intrinsic fuzziness system's strength in HIV-infected patients. question considered CD4+ T-cells cytotoxic T-lymphocytes (CTLs). dynamic behavior within three groups patients with weak, moderate, strong systems analyzed compared. Moreover, approximate explicit solutions proposed derived using...

The performance index of both the state and control variables with a constrained dynamic optimization problem fractional order system fixed final Time have been considered here. This paper presents general formulation solution scheme class optimal problems. method is based upon finding numerical Hamilton–Jacobi–Bellman equation, corresponding to this problem, by Legendre–Gauss collocation method. main reason for using technique its efficiency simple application. Also, in work, we use...

The Bezier curves are presented to solve the optimal control problem with pantographs delays. Direct algorithm for solving this is given. We have chosen as piecewise polynomials of degree n, and determine on [t0, tf] by n+1 points. Numerical examples illustrate that applicable, very easy use.

The type-2 fuzzy logic system permits us to model uncertainties existing in membership functions.Accordingly, this study aims propose a linear and piecewise framework for an interval regression based on the possibilistic models.In model, vagueness is minimized, under circumstances where hcut of observed value included predicted value.In both primary secondary function fit value.Developing proposed makes it helpful dealing with fluctuating data.This without additional complexities,...

This paper presents a new approach for solving class of infinite horizon nonlinear optimal control problems (OCPs). In this approach, two-point boundary value problem (TPBVP), derived from Pontryagin’s maximum principle, is transformed into sequence linear time-invariant TPBVPs. Solving the latter in recursive manner provides law and trajectory form uniformly convergent series. Hence, to obtain solution, only techniques ordinary differential equations are employed. An efficient algorithm...

Various aspects of the interaction HIV with human immune system can be modeled by a ordinary differential equations. This model is utilized, and multiobjective optimal control problem (MOOCP) proposed to maximize CD4+ T cells population minimize both viral load drug costs. The weighted sum method used, continuous Pareto solutions are derived solving corresponding optimality system. Moreover, predictive (MPC) strategy applied, final goal implementing structured treatment interruptions (STI)...

This paper presents a new idea to solve fractional differential equations and optimal control problems. The derivative is defined in the Grunwald–Letnikov sense. method based on linear programming problem. In this paper, by using first concept of derivatives, we will suggest where an equation with changed problem, solving it be obtained. Actually suggested minimization total error. Some numerical examples are provided confirm accuracy proposed method.