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• MakaleYalnız künye2017Scopus SJRQ2/r/gumushane/15343
  Solutions around a regular α singular point of a sequential conformable fractional differential equation

  Unal, Emrah; Gokdogan, Ahmet; Celik, Ercan

  In this work, firstly, some concepts of conformable fractional calculus in literature are given. Secondly, definitions of α-analytic point, α-ordinary point and regular α singular point are presented. Finally, the fractional power series solutions are given around a regular-singular point, in the case of variable coefficients for homogeneous sequential linear conformable fractional differential equations of order 2α.

  AtıfScopus9·WoS9

  İncele
• MakaleAçık Erişim2017Scopus SJRQ2/r/gumushane/15209
  Solution of conformable fractional ordinary differential equations via differential transform method

  Ünal, Emrah; Gökdoğan, Ahmet

  Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in (Khalil et al., 2014). Then, the fractional versions of chain rules, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions is developed in (Abdeljawad, 2015). In this paper, we give conformable fractional differential transform method and its application to conformable fractional differential equations.

  AtıfScopus134·WoS116·OpenAlex140

  İncele
• MakaleYalnız künye2017Scopus SJRQ2/r/gumushane/15136
  The operator method for local fractional linear differential equations

  Ünal, Emrah; Gökdoğan, Ahmet; Cumhur, İshak

  In this work, we give the particular solution for nonhomogeneous sequential linear conformable fractional differential equations with constant coefficients by using the operator method.

  AtıfScopus9·WoS7·OpenAlex9

  İncele
• MakaleYalnız künye2016/r/gumushane/18552
  Conformable Fractional Chebyshev Equations and Fractional Chebyshev Polynomials

  Gökdoğan, Ahmet; Ünal, Emrah

  In this work, we give the fractional power series solutions around = 0 -ordinary point of conformable fractional first and second kind Chebyshev differential equations. We present first and second kind fractional Chebyshev polynomials using by these solutions. Finally, we present certain property of fractional first and second kind Chebyshev polynomials.

  İncele
• MakaleAçık Erişim2016Scopus SJRQ3/r/gumushane/15224
  Existence and uniqueness theorems for sequential linear conformable fractional differential equations

  Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

  Recently, a new definition of fractional derivative called as the conformable fractional derivative which based on limits introduced by Khalil et al (2014). Later, Abdeljawad (2015) improved these definitions and gave the basic concepts in this new fractional calculus. In this paper, we generalize Abel's formula and Wronskian determinant definition and establish existence and uniqueness theorems for sequential linear conformable fractional differential equations.

  AtıfScopus27·WoS26·OpenAlex40

  İncele
• MakaleYalnız künye2016Scopus SJRQ2/r/gumushane/15106
  Multiplicative Laplace transform and its applications

  Yalcin, Numan; Celik, Ercan; Gokdogan, Ahmet

  In this work, taking definitions and properties of Laplace transform in classical analysis as a basis, we give some basic definitions and properties of the multiplicative Laplace transform. In addition, solutions of some multiplicative differential equations are obtained by the help of this transform.

  AtıfScopus23·WoS23·OpenAlex32

  İncele
• BildiriYalnız künye2014/r/gumushane/15452
  A new approach stereo based palmprint extraction in unrestricted postures

  Bingol, Ozkan; Ekinci, Murat; Gokdogan, Ahmet

  Regarding the palms recognition system studies, despite achieving a high success rate, hygiene problems in systems with contact and problems arising from changes in the alignment of the hand pose in non-contact ones have been encountered. To resolve these problems, 3D palmprint recognition systems have been developed, however these systems have not had the opportunity to spread due to expensive technologies used as well as low screening rates. In this study, to calculate the position and orientation of a palm in 3D space, a stereo camera system is proposed, with the help of these values by adjusting the geometric image of the palm is converted to a 2D environment. From these images, patterns used for recognition are extracted by using Active Appearance Models. Thus a non-contact system has been achieved, but also patterns that can be used by powerful 2D recognition systems have also been produced.

  AtıfScopus7·WoS5·OpenAlex5

  İncele
• MakaleYalnız künye2013Scopus SJRQ2/r/gumushane/15770
  Adaptive multi-step differential transformation method to solve ODE systems

  Gökdoǧan, Ahmet; Merdan, Mehmet

  In this paper, it is given a fast algorithm to solve chaotic differential systems using the multi-step differential transforms method (MsDTM). The approach is applied to a number of chaotic nonlinear differential equations and numerical results are given. Performance analyses reveal that the proposed approach is an efficiency tool to solve using fewer time step to the considered equation systems.

  AtıfScopus6·WoS4

  İncele
• MakaleAçık Erişim2013Scopus SJRQ2/r/gumushane/15693
  On numerical solution to fractional non-linear oscillatory equations

  Merdan, Mehmet; Gökdoǧan, Ahmet; Yildirim, Ahmet

  In this article, the multi-step differential transform method (MsDTM) is applied to give approximate solutions of nonlinear ordinary differential equation such as fractional-non-linear oscillatory and vibration equations. The results indicate that the method is very effective and sufficient for solving non-linear differential equations of fractional order.

  AtıfScopus14·WoS11·OpenAlex11

  İncele
• MakaleYalnız künye2013Scopus SJRQ2/r/gumushane/15650
  A multistage variational iteration method for solution of delay differential equations

  Gökdoǧan, Ahmet; Merdan, Mehmet; Ertürk, Vedat Suat

  In this paper, the approximate solution of delay differential equations is obtained by a reliable algorithm based on an adaptation of the classical variational iteration method (VIM), which is called the multi-stage variational iteration method (MSVIM). Examples are carried out and numerical results with comparison to exact solutions, VIM and MATLAB dde23 solver are given. The comparison reveals that the MSVIM is a promising tool to solve delay differential equations.

  AtıfScopus3·WoS2·OpenAlex4

  İncele