Open Access

Articles

Article ID: 2452

OPTIMIZING ROYALTY PAYMENTS FOR MAXIMUM ECONOMIC BENEFIT: A CASE STUDY UTILIZING MODIFIED SHOOTING AND DISCRETIZATION METHODS

by Wan, Suliadi FirdausSufahani, Mahmod Mohamad, Norhaslinda ZainalAbidin

Advances in Differential Equations and Control Processes, Vol.31, No.4, 2024; 9 Views

This research delves into the application of the modified shooting method for the numerical resolution of non-standard optimal control (OC) problems. More precisely, it concentrates on scenarios where the final state value component remains unknown and unconstrained, leading to a non-zero final shadow value or costate variable. Moreover, the objective function involved a piecewise royalty function, which poses a challenge due to its lack of differentiability within a specific time interval. Consequently, the novel modified shooting method was employed to ascertain the elusive final state value. The model’s differentiability is maintained throughout by adopting a continuous hyperbolic tangent (tanh) approximation. In addition, the construction of the Sufahani-Ahmad-Newton-Golden-Royalty Algorithm (SANGRA) and Sufahani-Ahmad-Powell-Golden-Royalty Algorithm (SAPGRA) was accomplished using the C++ programming language to formulate the problem. The outcomes of these algorithms, satisfying the criteria for optimality, were juxtaposed with non-linear programming (NLP) techniques such as Euler and Runge-Kutta, aside from Trapezoidal and Hermite-Simpson approximations. This groundbreaking discovery carries extensive practical implications as it propels the field forward and ensures the application of contemporary problem-solving methodologies. Moreover, the study underscores the significance of fundamental theory in effectively tackling current economic challenges.

Open Access

Articles

Article ID: 2453

A PROBLEM IN FRACTIONAL ORDER THERMO-VISCOELASTICITY THEORY FOR A POLYMER MICRO-ROD WITH AND WITHOUT ENERGY DISSIPATION

by Mohamed H.Hendy, Magdy A.Ezzat, Esraa M.Al-lobani, Ahmed S.Hassan

Advances in Differential Equations and Control Processes, Vol.31, No.4, 2024; 6 Views

A new study has been developed that considers the size-dependent interaction between viscoelastic deformation and thermal fields, incorporating the fractional heat conduction law with and without energy dissipation. The model is used for a particular one-dimensional problem involving a polymer micro-rod of arbitrary length experiencing three different types of thermal loading without the presence of any heat source. The study uses Laplace transforms and numerical inversion to examine how fractional order, nonlocal elasticity, and nonlocal thermal conduction impact thermal dispersion and thermo-viscoelastic response. Comparative numbers demonstrate the effects of various parameters. Findings demonstrate that nonlocal thermal and viscoelastic characteristics have a significant impact on all recorded field values, offering possible suggestions for the creation and assessment of thermal-mechanical attributes in nanoscale devices.

Open Access

Articles

Article ID: 2454

GENERALIZED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY TWO MUTUALLY INDEPENDENT FRACTIONAL BROWNIAN MOTIONS

by Yaya SAGNA, Lamine SYLLA, Sadibou AIDARA

Advances in Differential Equations and Control Processes, Vol.31, No.4, 2024; 4 Views

This paper deals with a class of generalized backward stochastic differential equations driven by two mutually independent fractional Brownian motions (FGBSDEs in short). The existence and uniqueness of solutions for FGBSDE as well as a comparison theorem are obtained.

Open Access

Articles

Article ID: 2455

AN INNOVATIVE METHOD FOR SOLVING LINEAR AND NONLINEAR FRACTIONAL TELEGRAPH EQUATIONS

by Mona Magzoub, Tarig M.Elzaki, Mourad Chamekh

Advances in Differential Equations and Control Processes, Vol.31, No.4, 2024; 6 Views

This work investigates and solves the time-fractional telegraph equations (TFTEs) occurring in electromagnetism, which serve as mathematical models in several practically significant applied research domains. Elzaki transform (ET) is employed in this process. Caputo sense describes fractional derivatives. Solutions of TFTEs were found in an easy-to-understand, step-by-step way using ET. In addition, instances are given to show how the phrase can be applied and how valid it is for the problem-solving form. The exact solutions and the analytical solutions accord well for the tested problems. This work also discusses the convergence of the ET technique to the exact solution of TFTEs. Several examples of linear and nonlinear TFTEs are used to demonstrate the suggested methodology. The novel technique’s results show that it is an effective way to solve TFTEs, and it makes the procedure easier.

Open Access

Articles

Article ID: 2456

NECESSARY CONDITIONS FOR OPTIMALITY IN ONE NONSMOOTH OPTIMAL CONTROL PROBLEM FOR GOURSAT-DARBOUX SYSTEMS

by Aysel T.Ramazanova

Advances in Differential Equations and Control Processes, Vol.31, No.4, 2024; 5 Views

We consider a nonsmooth optimal control problem described by a system of second-order hyperbolic equations with Goursat boundary conditions. A number of necessary optimality conditions are proved in terms of directional derivatives.

Open Access

Articles

Article ID: 2448

REGULARIZATION OF THE INVERSE PROBLEM WITH THE D’ALEMBERT OPERATOR IN AN UNBOUNDED DOMAIN DEGENERATING INTO A SYSTEM OF INTEGRAL EQUATIONS OF VOLTERRA TYPE

by T. D.Omurov, K. R.Dzhumagulov

Advances in Differential Equations and Control Processes, Vol.31, No.4, 2024; 7 Views

In this paper, we study the inverse problem for the wave equation with the second-order d’Alembert operator in an unbounded domain in a space with a non-uniform metric. For physical applications, inverse problems for second-order partial differential equations are of particular interest. Such inverse problems are encountered in the study of wave processes, processes of electromagnetic interactions, as well as in various reduction processes. Moreover, if there are external acting forces with respect to the indicated equations that allow additional information about the solution of the original equations, then we obtain classes of inverse problems of a coefficient nature with the d’Alembert operator, which are of particular interest to scientists in this field, in which the results of this article are relevant. Also, the relevance of the problem under study is due to the fact that it is an inverse problem, where the sought quantities are the causes of some known consequences of a particular process. Whereas for direct problems, the methods for solving are well known. Thus, this paper provides a solution to the inverse problem of mathematical physics with a hyperbolic operator and generalizes existing results.