Mojtaba Hajipour

• Dr.
• Professor (Assistant) at Sahand University of Technology

Time-delay fractional optimal control problems (OCPs) are an important research area for developing effective control and optimization strategies to address complex phenomena occurring in various natural sciences, such as physics, chemistry, biology, and engineering. By considering fractional OCPs with time delays, we can design control strategies...

The aim of this paper is to investigate some second- and third-order numerical methods for solving the Volterra integral equations (VIEs) of the second kind. The proposed numerical methods preserve the V_0-stability property for both single and system of the VIEs. Numerical simulations show that these methods are successful for various types of the...

The aim of this paper is to investigate some V0-stable numerical methods based on the θ-method for solving the Volterra integral equations (VIEs) of the second kind. The proposed V0-stable methods have the second- and third-order of acuuracy, and guarantee the V0-stability property for VIEs. Numerical simulations show that these methods are succsee...

In this paper, in order to determine the radiation field a Cauchy problem associate with the Helmholtz equation in an infinite strip domain is investigated. This problem lies in the range of classical problems and is extremely ill-posed in the sense that a small perturbation in the Cauchy data may cause a dramatically large error in the solution. A...

The main focus of this paper is on studying an order optimal regularization scheme based on the Meyer wavelets method to solve the analytic continuation problem in the high-dimensional complex domain := {x + iy ∈ C N : x ∈ R N , y ≤ y 0 , y, y 0 ∈ R N + }. This problem is exponentially ill-posed and suffers from the Hadamard's instability. Theoreti...

This manuscript deals with a regularization technique for a generalized space-fractional backward heat conduction problem (BHCP) which is well-known to be extremely ill-posed. The presented technique is developed based on the Meyer wavelets in retrieving the solution of the presented space-fractional BHCP. Some sharp optimal estimates of the Hölder...

The aim of this paper is to investigate an efficient numerical method based on a novel shifted piecewise cosine basis for solving Volterra–Fredholm integral equations of the second kind. Using operational matrices of integration for the proposed basis functions, this integral equation is transformed into a system of nonlinear algebraic equations. T...

The principle result of this paper is the following disturbance rejection control scheme for a class of nonlinear dynamical systems. By using the internal model principle, the problem of disturbance damping control is converted into a nonlinear quadratic regulator (NQR) problem for an undisturbed augmented system. Then, an iterative technique is de...

The aim of this manuscript is to investigate an accurate discretization method to solve the one-, two-, and three-dimensional highly nonlinear Bratu-type problems. By discretization of the nonlinear equation via a fourth-order nonstandard compact finite difference formula, the considered problem is reduced to the solution of a highly nonlinear alge...

The purpose of this paper is to study the existence and uniqueness of the solution of nonlinear fractional differential equations with Mittag–Leffler nonsingular kernel. Two numerical methods to solve this problem are designed, and their stability and error estimates are investigated by discretizing the convolution integral and using the Grönwall’s...

The aim of this paper is to develop an accurate discretization technique to solve a class of variable-order fractional (VOF) reaction-diffusion problems. In the spatial direction, the problem is first discretized by using a compact finite difference operator. Then, a weighted-shifted Grünwald formula is applied for the temporal discretization of fr...

The nutrition of pregnant women is crucial for giving birth to a healthy baby and even for the health status of a nursing mother. In this paper, the poor nutrition in the life cycle of humans is explored in the fractional sense. The proposed model is examined via the Caputo fractional operator and a new one with Mittag–Leffler (ML) nonsingular kern...

This paper presents a class of semi-implicit finite difference weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear heat equation. For the discretization of second-order spatial derivatives, a sixth-order modified WENO scheme is directly implemented. This scheme preserves the positivity principle and rejects spurious oscill...

This manuscript mainly focuses on the construction, dynamic analysis and control of a new fractional-order financial system. The basic dynamical behaviors of the proposed system are studied such as the equilibrium points and their stability, Lyapunov exponents, bifurcation diagrams, phase portraits of state variables and the intervals of system par...

The aim of this manuscript is to investigate an efficient iterative approach for the nonlinear fractional optimal control problems affected by the external persistent disturbances. For this purpose, first the internal model principle is employed to transform the fractional dynamic system with disturbance into an undisturbed system with both integer...

This paper is concerned with a backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite “strip”. This problem is drastically ill-posed which is caused by the amplified infinitely growth in the frequency components. A new regularization method based on the Meyer wavelet technique is developed to solve the consid...

The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag–Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fracti...

In this paper, we formulate a new nonstandard finite difference (NSFD) scheme to study the dynamic treatments of a class of fractional chaotic systems. To design the new proposed scheme, an appropriate nonlocal framework is applied for the discretization of nonlinear terms. This method is easy to implement and preserves some important physical prop...

In this work, an accurate regularization technique based on the Meyer wavelet method is developed to solve the ill-posed backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite "strip". In principle, the extremely ill-posedness of the considered problem is caused by the amplified infinitely growth in the frequ...

The aim of this study is to develop an efficient iterative approach for solving a class of time-delay optimal control problems with time-varying delay and external persistent disturbances. By using the internal model principle, the original time-delay model with disturbance is first converted into an augmented system without any disturbance. Then,...

This article presents a novel iterative eigenvalue decomposition approach for solving the optimal control problem of time-delay systems. In this approach, the original time-delay optimal control problem is transformed into a sequence of decoupled linear first-order initial value problems without delay and advance terms. Solving the derived sequence...

This paper mainly focuses on the analysis of a hyperchaotic financial system as well as its chaos control and synchronization. The phase diagrams of the above system are plotted and its dynamical behaviours like equilibrium points, stability, hyperchaotic attractors and Lyapunov exponents are investigated. In order to control the hyperchaos, an eff...

This article presents an efficient parallel processing approach for solving the optimal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin's maximum principle is first transformed into a sequence of lower-order decoupled lin...

In this paper, an efficient finite difference method is presented for the solution of time-delay optimal control problems with time-varying delay in the state. By using the Pontryagin's maximum principle, the original time-delay optimal control problem is first transformed into a system of coupled two-point boundary value problems involving both de...

This paper presents a recursive shooting method for solving the optimal control problem of linear time-varying systems with state time-delay. In this approach, the original time-delay optimal control problem is first transformed into a sequence of linear two-point boundary value problems (TPBVPs) without delay and advance terms. Then, by using a sh...

In this paper, we propose a high accurate method based on non-standard Runge–Kutta (NRK), modified weighted essentially non-oscillatory (MWENO) and grid stretching methods to solve the Black–Scholes equation with discontinuous final condition. For the spatial and temporal discretization of the Black–Scholes equation, the MWENO method and the NRK me...

In this paper we present efficient high-order methods based on weighted essentially non-oscillatory (WENO) technique and backward differencing formula (BDF) to solve the European and American put options of the Black-Scholes equation. In order to achieve high-order convergent and prevent the appearance of spurious solutions close to non-smooth poin...

In this paper, we propose a stable high accurate hybrid scheme based on nonstandard Runge–Kutta (NRK) and modified weighted essentially non-oscillatory (MWENO) techniques for nonlinear degenerate parabolic partial differential equations. The necessary stability condition for the combination of a Runge–Kutta and MWENO scheme is given. The stability...

In this work, we investigate the new preconditioner of the Tau method, introduced by Ghoreishi and Mohammad Hosseini [13], on systems of ODEs. With a different and relatively straightforward view on the Tau formulation of systems of ODEs this preconditioner is reformulated and explained. An error analysis of the method is also addressed. Some numer...

In this article, the Exp-function method is applied to nonlinear Burgers equation and special fifth-order partial differential equation. Using this method, we obtain exact solutions for these equations. The method is straightforward and concise, and its applications are promising. This method can be used as an alternative to obtain analytical and a...