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Ahmet Gökdoğan

Bio: Ahmet Gökdoğan is an academic researcher from Gümüşhane University. The author has contributed to research in topics: Fractional calculus & Conformable matrix. The author has an hindex of 12, co-authored 34 publications receiving 510 citations.

Papers
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Journal ArticleDOI
01 Jan 2017-Optik
TL;DR: In this paper, a conformable fractional differential transform method and its application to conformable fractions of differential equations is given. But the method is not suitable for the case of fractional derivatives of chain rules.

106 citations

Journal ArticleDOI
TL;DR: A modified VIM (MVIM), based on the use of Pade approximants is proposed, to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as a model for HIV infection of CD4 + T cells.
Abstract: In this article, a variational iteration method (VIM) is performed to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as a model for HIV infection of CD4 + T cells. A modified VIM (MVIM), based on the use of Pade approximants is proposed. Some plots are presented to show the reliability and simplicity of the methods.

84 citations

Journal ArticleDOI
TL;DR: In this paper, the modified differential transform method (MDTM) is used to increase the accuracy and accelerate the convergence rate of truncated series solution getting by the DTM, which can be obtained from DTM applied to Laplace, inverse Laplace transform and Pade approximant.

65 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented a reliable algorithm based on the standard differential transformation method (DTM), which is called the multi-stage differential transformation (MsDTM) for solving Hantavirus infection model.

53 citations

Journal ArticleDOI
TL;DR: A comparison between the MsD TM and the adaptive MsDTM reveals that the proposed approach is an efficiency tool for solving the considered equations using fewer time steps.

43 citations


Cited by
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Journal ArticleDOI
TL;DR: The present paper introduces memristor-based fractional-order neural networks and establishes the conditions on the global Mittag-Leffler stability and synchronization are established by using Lyapunov method.

459 citations

Journal ArticleDOI
TL;DR: In this article, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type, which is efficient in modeling a class of concentrations in the complex transport process.
Abstract: In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

217 citations

Journal ArticleDOI
01 Aug 2020
TL;DR: A new definition of fuzzy fractional derivative, so-called fuzzy conformable, is proposed and the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.
Abstract: The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.

157 citations

Journal ArticleDOI
TL;DR: Some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems are proposed and a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition.
Abstract: Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.

152 citations

Journal ArticleDOI
01 Jan 2017-Optik
TL;DR: In this paper, a conformable fractional differential transform method and its application to conformable fractions of differential equations is given. But the method is not suitable for the case of fractional derivatives of chain rules.

106 citations