Yazarlar

• Cona, Lale(2)

• MakaleAçık Erişim2025/r/gumushane/16740
  A 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.

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• MakaleAçık Erişim2024Scopus SJRQ2/r/gumushane/11620
  Convergence 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.

  AtıfWoS1·OpenAlex1

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