Browsing by Author "Georgiev, Svetlin G."

Now showing 1 - 6 of 6

Citation - WoS: 1
Citation - Scopus: 2
Existence of Solutions for First Order Impulsive Periodic Boundary Value Problems on Time Scales
(Univ Nis, Fac Sci Math, 2023) Georgiev, Svetlin G.; Akgol, Sibel Dogru; Kus, M. Eymen
In this paper we study a class of first order impulsive periodic boundary value problems on time scales. We give conditions under which the considered problem has at least one and at least two solutions. The arguments are based upon recent fixed point index theory in cones of Banach spaces for a k-set contraction perturbed by an expansive operator. An example is given to illustrate the obtained result.
Citation - WoS: 1
Citation - Scopus: 2
Existence of Solutions for Odd-Order Multi-Point Impulsive Boundary Value Problems on Time Scales
(Walter de Gruyter Gmbh, 2022) Georgiev, Svetlin G.; Akgol, Sibel Dogru; Kus, Murat Eymen
Using a fixed point theorem due to Schaefer, the existence of solutions for an odd-order m-point impulsive boundary value problem on time scales is obtained. The problem considered is of general form, where both the differential equation and the impulse effects are nonlinear. Illustrative examples are provided.
Citation - WoS: 1
Citation - Scopus: 2
Existence of Solutions for Third Order Multi Point Impulsive Boundary Value Problems on Time Scales
(Univ Miskolc inst Math, 2022) Georgiev, Svetlin G.; Akgol, Sibel D.; Kus, M. Eymen
In this paper, we obtain sufficient conditions for existence of solutions of a third order m-point impulsive boundary value problem on time scales. To the best of our knowledge, there is hardly any work dealing with third order multi point dynamic impulsive BVPs. The reason may be the complex arguments caused by both impulsive perturbations and calculations on time scales. As an application, we give an example demonstrating our results.
Citation - WoS: 4
Citation - Scopus: 6
Lagrange Interpolation on Time Scales
(Wilmington Scientific Publisher, Llc, 2022) Georgiev, Svetlin G.; Erhan, Inci M.
In this paper, we introduce the Lagrange interpolation polynomials on time scales. We define an alternative type of interpolation functions called s-Lagrange interpolation polynomials. We discuss some properties of these polynomials and show that on some special time scales, including the set of real numbers, these two types of interpolation polynomials coincide. We apply our results on some particular examples.
Citation - WoS: 11
Citation - Scopus: 20
The Taylor Series Method and Trapezoidal Rule on Time Scales
(Elsevier Science inc, 2020) Georgiev, Svetlin G.; Erhan, Inci M.
The Taylor series method for initial value problems associated with dynamic equations of first order on time scales with delta differentiable graininess function is introduced. The trapezoidal rule for the same types of problems is derived and applied to specific examples. Numerical results are presented and discussed. (c) 2020 Elsevier Inc. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 2
The Taylor Series Method of Order p and Adams-Bashforth Method on Time Scales
(Wiley, 2023) Georgiev, Svetlin G.; Erhan, Inci M.
A recent study on the Taylor series method of second order and the trapezoidal rule for dynamic equations on time scales has been continued by introducing a derivation of the Taylor series method of arbitrary order p$$ p $$ on time scales. The error and convergence analysis of the method is also obtained. The 2-step Adams-Bashforth method for dynamic equations on time scales is concluded and applied to examples of initial value problems for nonlinear dynamic equations. Numerical results are presented and discussed.