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Journal of Function Spaces and Applications
Volume 2012, Article ID 214961, 13 pages
http://dx.doi.org/10.1155/2012/214961
Research Article

Novel Identities for 饾憺 -Genocchi Numbers and Polynomials

Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaziantep, Turkey

Received 26 February 2012; Revised 25 April 2012; Accepted 9 May 2012

Academic Editor: Gestur Ólafsson

Copyright © 2012 Serkan Araci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [20 citations]

The following is the list of published articles that have cited the current article.

  • Abdulnasir Isah, and Chang Phang, “On Genocchi operational matrix of fractional integration for solving fractional differential equations,” vol. 1795, pp. 020015, . View at PublisherView at Google Scholar
  • Erdoğan Şen, Mehmet Acikgoz, Jong Jin Seo, Serkan Araci, and Kamil Oruçoğlu, “Existence and Uniqueness of Positive Solutions of Boundary-Value Problems for Fractional Differential Equations with -Laplacian Operator and Identities on the Some Special Polynomials,” Journal of Function Spaces and Applications, vol. 2013, pp. 1–11, 2013. View at PublisherView at Google Scholar
  • Taekyun Kim, Dae San Kim, Seog-Hoon Rim, and Dmitry V. Dolgy, “Some identities of frobenius-type eulerian polynomials arising from umbral calculus,” International Journal of Mathematical Analysis, vol. 7, no. 53-56, pp. 2637–2644, 2013. View at PublisherView at Google Scholar
  • Serkan Araci, “Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus,” Applied Mathematics and Computation, vol. 233, pp. 599–607, 2014. View at PublisherView at Google Scholar
  • Serkan Araci, Mehmet Acikgoz, and Erdogan Sen, “On the von Staudt-Clausen's theorem associated with q-Genocchi numbers,” Applied Mathematics and Computation, vol. 247, pp. 780–785, 2014. View at PublisherView at Google Scholar
  • Serkan Araci, Erdoǧan Şen, and Mehmet Acikgoz, “Theorems on genocchi polynomials of higher order arising from genocchi basis,” Taiwanese Journal of Mathematics, vol. 18, no. 2, pp. 473–482, 2014. View at PublisherView at Google Scholar
  • Serkan Araci, Srivastava, Armen Bagdasaryan, and Cenap Özel, “New symmetric identities involving q-zeta type functions,” Applied Mathematics and Information Sciences, vol. 8, no. 6, pp. 2803–2808, 2014. View at PublisherView at Google Scholar
  • Serkan Araci, Mehmet Acikgoz, and Erdoğan Şen, “Some New Formulae for Genocchi Numbers and Polynomials Involving Bernoulli and Euler Polynomials,” International Journal of Mathematics and Mathematical Sciences, vol. 2014, pp. 1–7, 2014. View at PublisherView at Google Scholar
  • Serkan Araci, Erdoğan Şen, Mehmet Acikgoz, and Kamil Oruçoğlu, “Identities involving some new special polynomials arising from the applications of fractional calculus,” Applied Mathematics and Information Sciences, vol. 9, no. 5, pp. 2657–2662, 2015. View at PublisherView at Google Scholar
  • Erkan Aʇyüz, Mehmet Acikgoz, and Serkan Araci, “A symmetric identity on the q-Genocchi polynomials of higher-order under third dihedral group D3,” Proceedings of the Jangjeon Mathematical Society, vol. 18, no. 2, pp. 177–187, 2015. View at PublisherView at Google Scholar
  • Mehmet Kir, Hemen Dutta, Mehmet Acikgoz, and Serkan Araci, “Identities on Some Special Poynomials Derived from the Concepts of $$ {\it n}$$ n -Normed Structures, Accretive Operators and Contraction Mappings,” Iranian Journal of Science and Technology, Transactions A: Science, 2016. View at PublisherView at Google Scholar
  • Chang Phang, and Abdulnasir Isah, “Genocchi Wavelet-like Operational Matrix and its Application for Solving Non-linear Fractional Differential Equations,” Open Physics, vol. 14, no. 1, pp. 463–472, 2016. View at PublisherView at Google Scholar
  • Mehmet Acikgoz, Armen Bagdasaryan, and Serkan Araci, “On the properties of q-Bernstein-type polynomials,” Applied Mathematics and Information Sciences, vol. 11, no. 5, pp. 1259–1268, 2017. View at PublisherView at Google Scholar
  • Abdulnasir Isah, and Chang Phang, “Operational matrix based on Genocchi polynomials for solution of delay differential equations,” Ain Shams Engineering Journal, 2017. View at PublisherView at Google Scholar
  • Jian Rong Loh, and Chang Phang, “A new numerical scheme for solving system of Volterra integro-differential equation,” Alexandria Engineering Journal, 2017. View at PublisherView at Google Scholar
  • Abdulnasir Isah, and Chang Phang, “New Operational Matrix of Derivative for Solving Non-linear Fractional Differential Equations Via Genocchi Polynomials,” Journal of King Saud University - Science, 2017. View at PublisherView at Google Scholar
  • Abdulnasir Isah, Chang Phang, and Piau Phang, “Collocation Method Based on Genocchi Operational Matrix for Solving Generalized Fractional Pantograph Equations,” International Journal of Differential Equations, vol. 2017, pp. 1–10, 2017. View at PublisherView at Google Scholar
  • Jian Rong Loh, Chang Phang, and Abdulnasir Isah, “New Operational Matrix via Genocchi Polynomials for Solving Fredholm-Volterra Fractional Integro-Differential Equations,” Advances in Mathematical Physics, vol. 2017, pp. 1–12, 2017. View at PublisherView at Google Scholar
  • Haniye Dehestani, Yadollah Ordokhani, and Mohsen Razzaghi, “A numerical technique for solving various kinds of fractional partial differential equations via Genocchi hybrid functions,” Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019. View at PublisherView at Google Scholar
  • Sachin Kumar, and Prashant Pandey, “A Legendre spectral finite difference method for the solution of non-linear space-time fractional Burger’s–Huxley and reaction-diffusion equation with Atangana–Baleanu derivative,” Chaos, Solitons & Fractals, vol. 130, pp. 109402, 2020. View at PublisherView at Google Scholar