Yazarlar
- Cona, Lale(4)
- Sengül, Kadir(1)
- Şengül, Kadir(1)
Yayınlar
- MakaleAçık Erişim2025A FIXED POINT APPROACH TO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS: CONVERGENCE AND DATA DEPENDENCE
Cona, Lale
Fractional calculus, which involves derivatives and integrals of non-integer order, is widely used in modeling real-world problems in science and engineering. This study focuses on solving fractional integro-differential equations using Picard's three-step iteration algorithm. We apply Picard's three-step iteration algorithm to approximate solutions and show that it converges strongly. The method is shown to be not only efficient in approximating solutions but also robust with respect to perturbations in the initial data and operators, demonstrating its data dependence. A numerical example is provided to illustrate the theoretical results and to confirm the applicability and reliability of the proposed approach.
- MakaleYayıncıda açık erişim2024Solutions of linear Fredholm integral equations with the three- step iteration method
Cona, Lale; Sengül, Kadir
In this article, the solution of the second type of nonhomogeneous linear Fredholm integral equations is investigated using a three-step iteration algorithm. It has been shown that the sequences obtained from this algorithm converge to the solution of the mentioned equations. Morever, data dependency is obtained for the second type of nonhomogeneous linear Fredholm integral equations. This result is supported by an example.
- MakaleAçık Erişim2024Convergence and data dependence results of the nonlinear Volterra integral equation by the Picard's three step iteration
Cona, Lale
Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature. The purpose of this paper was to study using this iteration algorithm for the solution of nonlinear Volterra integral equations. It was investigated that the sequences obtained from this iteration algorithm converged to the solution of nonlinear Volterra integral equations. Moreover, data dependence was obtained for nonlinear Volterra integral equations. An example was given that confirmed the applicability of the newly proven theorems.
- MakaleAçık Erişim2023On Data Dependency and Solutions of Nonlinear Fredholm Integral Equations with the Three-Step Iteration Method
Cona, Lale; Şengül, Kadir
In this study, the solution of the second type of homogeneous nonlinear Fredholm integral equations is investigated using a three-step iteration algorithm. In other words, it has been shown that the sequences obtained from this algorithm converge to the solution of the mentioned equations. Also, data dependency is obtained for the second type of homogeneous nonlinear Fredholm integral equations and this result is supported by an example.