Advances in Differential Equations and Control Processes

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Explore the latest advances in differential equations and their applications in control processes. Discover new theories and methods for complex system analysis.

Advances in Differential Equations and Control Processes Cover

Articles in this Journal

ON THE EXISTENCE OF CLASSICAL SOLUTION TO ONE-DIMENSIONAL FOURTH ORDER SEMILINEAR EQUATIONS

In this paper, we prove the existence in small of classical solution of one-dimensional mixed problem for one class of fourth order semilinear Sobolev type equations by combining the generalized contracted mapping principle with Schauder’s...

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HOMOTOPY PERTURBATION METHOD TO SOLVE DUFFING-VAN DER POL EQUATION

In this paper, the Homotopy Perturbation Method (HPM) and the Regular Perturbation Method (RPM) are used to study Duffing-Van der Pol equation. Then we compare the solutions obtained by these two methods. Received: February 15, 2024Accepte...

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AN EFFICIENT SCHEME TO SOLVE FOURTH ORDER NONLINEAR TRIPLY SINGULAR FUNCTIONAL DIFFERENTIAL EQUATION

We present a novel mathematical model based on the fourth order multi-singular nonlinear functional differential equations. This designed nonlinear functional model has singularities at three points, making the model more complicated and h...

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SUMUDU AND ELZAKI INTEGRAL TRANSFORMS FOR SOLVING SYSTEMS OF INTEGRAL AND ORDINARY DIFFERENTIAL EQUATIONS

We present two integral transforms namely Sumudu (ST) and Elzaki (ET) transforms for solving systems of integral and ordinary differential equations. Also, we study some properties of these transforms. The presented integral transforms are...

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OPTIMAL HARVESTING STRATEGY FOR PREY-PREDATOR MODEL WITH FISHING EFFORT AS A TIME VARIABLE

We study a prey-predator model with harvesting where the fishing effort is considered as a function of time. The analysis focuses on the equilibrium points and the optimal harvesting strategy. Received: February 21, 2024Accepted: April 18,...

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A NUMERICAL METHOD TO SOLVE THE VISCOSITY PROBLEM OF THE BURGERS EQUATION

Considering the viscosity problem of the Burgers equation, we give a numerical solution using the Cole-Hopf transformation. Received: January 12, 2024Accepted: February 27, 2024

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ON FINITE CHARACTER GEOMETRICAL PROPERTY OF THE DIFFERENTIAL REALIZATION OF NONSTATIONARY HYPERBOLIC SYSTEMS

Topological-algebraic investigation of the problem of existence of realization of finite-dimensional continuous dynamic processes in the class of second-order ordinary differential equations in a separable Hilbert space has been conducted....

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SOLVABILITY FOR CONTINUOUS CLASSICAL BOUNDARY OPTIMAL CONTROL OF COUPLE FOURTH ORDER LINEAR ELLIPTIC EQUATIONS

In this paper, we study continuous classical boundary optimal control problem for the couple fourth order of linear elliptic system with variable coefficients. The existence theorem of a unique couple vector state solution of the weak form...

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APPROXIMATED SOLUTIONS OF THE HOMOGENEOUS LINEAR FRACTIONAL DIFFUSION-CONVECTION-REACTION EQUATION

Our work focused on solving a homogeneous linear fractional diffusion, diffusion-convection and diffusion-convection-reaction model with various initial conditions and appropriate parameters. We used the Adomian decomposition method (ADM)...

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PERIODIC SOLUTIONS OF A SECOND-ORDER NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION

The article considers the problem of constructing a $2 \pi$-periodic solution of a quasilinear second-order integro-differential equation. Using the Green's function of bounded solutions on the number line, the integro-differential equatio...

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SUFFICIENCY-TYPE CONDITIONS FOR A TYPE OF STRICTLY DECREASING SOLUTIONS OF LINEAR CONTINUOUS-TIME DIFFERENTIAL SYSTEMS WITH BOUNDED POINT TIME-VARYING DELAYS

This paper investigates sufficiency-type conditions for strictly decreasing solutions of linear time-delay differential systems subject to a finite number of time-varying bounded point delays. The delay functions are not required to be tim...

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ANALYZING AND SIMULATING THE OSCILLATION IN MULTIDIMENSIONAL ODD COMPETITIVE SYSTEMS

We consider a multidimensional odd competitive model, which is a generalization to a multidimensional (more than two dimensions) case of both the P. Verhulst logistic model and the A. Lotka and V. Volterra competition model. Received: Apri...

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

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 d...

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THE SOME BLAISE ABBO (SBA) PLUS METHOD APPLIED TO FRACTIONAL NONLINEAR TIME SCHRÖDINGER EQUATIONS IN $d$ DIMENSION $(d = 1, 2,$ or $3)$ IN THE SENSE OF CAPUTO

In this paper, we have solved some time fractional Schrödinger equations of order $\alpha$ with $0<\alpha \leq 1$ in dimension $1, 2$ or $3$ in the sense of Caputo by the SBA plus method. This method is based on two principles (successi...