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Year 2020, Volume: 8 Issue: 2, 376 - 383, 27.10.2020

Mehmet Zeki Sarıkaya Abdullah Akkurt Hüseyin Budak Merve Esra Türkay Hüseyin Yildirim

Abstract

References

  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57–66.
  • [2] T. Abdeljawad, M. A. Horani and R. Khalil, Conformable fractional semigroup operators, Journal of Semigroup Theory and Applications vol. 2015 (2015) Article ID. 7.
  • [3] G.E. Andrews, R. Askey and R. Roy, Special functions, Encyclopedia of Mathematics and its Applications 71, Cambrige University, 1999.
  • [4] A. Atangana, D. Baleanu, and A. Alsaedi, New properties of conformable derivative, Open Math. 2015; 13: 889–898.
  • [5] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, 1974.
  • [6] R. Diaz and C. Teruel, q;k-Generalized gamma and beta functions, J. Nonlinear Math. Phys., 12 (2005), 118-134.
  • [7] R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Matematicas Vol. 15 No. 2(2007), pp. 179-192.
  • [8] R. Diaz, C. Ortiz and E. Pariguan, On the k-gamma q-distribution, Cent. Eur. J. Math., 8 (2010), 448-458.
  • [9] R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.
  • [10] R. Khalil, M. A. Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • [11] S. Mubeen and G. M Habibullah, k-Fractional integrals and application, Int. J. Contemp. Math. Sciences, Vol. 7, 2012, no. 2, 89 - 94.
  • [12] O.S. Iyiola and E.R.Nwaeze, Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl., 2(2), 115-122, 2016.
  • [13] M. A. Hammad and R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13( 3), 2014, 177-183.
  • [14] M. A. Hammad and R. Khalil, Abel’s formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Applications 13( 3), 2014, 177-183.
  • [15] U. N. Katugampola,New approach to generalized fractional integral, Appl. Math. Comput. 218 (2011), 860-865.
  • [16] U. N. Katugampola, A new approach to generalized fractional derivatives, Bul. Math. Anal.Appl., 6 (4) (2014), 1-15.
  • [17] U. N. Katugampola, A new fractional derivative with classical properties, e-print arXiv:1410.6535.

On Some Special Functions for Conformable Fractional Integrals

Year 2020, Volume: 8 Issue: 2, 376 - 383, 27.10.2020

Mehmet Zeki Sarıkaya Abdullah Akkurt Hüseyin Budak Merve Esra Türkay Hüseyin Yildirim

Abstract

In this paper, we introduce the $\left( \alpha ,k\right) $-gamma function$,\ \left( \alpha ,k\right) $-beta function, Pochhammer symbol $\left( x\right) _{n,k}^{\alpha }\ $and Laplace transforms for conformable fractional integrals. We prove several properties generalizing those satisfied by the classical gamma function, beta function and Pochhammer symbol. The results presented here would provide generalizations of those given in earlier works.                                                                                                                                                                                                                                                      

Keywords

Gamma function beta function Pochhammer symbol confromable fractional integrals

References

  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 (2015) 57–66.
  • [2] T. Abdeljawad, M. A. Horani and R. Khalil, Conformable fractional semigroup operators, Journal of Semigroup Theory and Applications vol. 2015 (2015) Article ID. 7.
  • [3] G.E. Andrews, R. Askey and R. Roy, Special functions, Encyclopedia of Mathematics and its Applications 71, Cambrige University, 1999.
  • [4] A. Atangana, D. Baleanu, and A. Alsaedi, New properties of conformable derivative, Open Math. 2015; 13: 889–898.
  • [5] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, 1974.
  • [6] R. Diaz and C. Teruel, q;k-Generalized gamma and beta functions, J. Nonlinear Math. Phys., 12 (2005), 118-134.
  • [7] R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Matematicas Vol. 15 No. 2(2007), pp. 179-192.
  • [8] R. Diaz, C. Ortiz and E. Pariguan, On the k-gamma q-distribution, Cent. Eur. J. Math., 8 (2010), 448-458.
  • [9] R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.
  • [10] R. Khalil, M. A. Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • [11] S. Mubeen and G. M Habibullah, k-Fractional integrals and application, Int. J. Contemp. Math. Sciences, Vol. 7, 2012, no. 2, 89 - 94.
  • [12] O.S. Iyiola and E.R.Nwaeze, Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl., 2(2), 115-122, 2016.
  • [13] M. A. Hammad and R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13( 3), 2014, 177-183.
  • [14] M. A. Hammad and R. Khalil, Abel’s formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Applications 13( 3), 2014, 177-183.
  • [15] U. N. Katugampola,New approach to generalized fractional integral, Appl. Math. Comput. 218 (2011), 860-865.
  • [16] U. N. Katugampola, A new approach to generalized fractional derivatives, Bul. Math. Anal.Appl., 6 (4) (2014), 1-15.
  • [17] U. N. Katugampola, A new fractional derivative with classical properties, e-print arXiv:1410.6535.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Zeki Sarıkaya

Abdullah Akkurt 0000-0001-5644-1276

Hüseyin Budak

Merve Esra Türkay 0000-0003-4429-2685

Hüseyin Yildirim 0000-0001-8855-9260

Publication Date October 27, 2020
Submission Date October 14, 2020
Acceptance Date October 21, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Sarıkaya, M. Z., Akkurt, A., Budak, H., Türkay, M. E., et al. (2020). On Some Special Functions for Conformable Fractional Integrals. Konuralp Journal of Mathematics, 8(2), 376-383.
AMA Sarıkaya MZ, Akkurt A, Budak H, Türkay ME, Yildirim H. On Some Special Functions for Conformable Fractional Integrals. Konuralp J. Math. October 2020;8(2):376-383.
Chicago Sarıkaya, Mehmet Zeki, Abdullah Akkurt, Hüseyin Budak, Merve Esra Türkay, and Hüseyin Yildirim. “On Some Special Functions for Conformable Fractional Integrals”. Konuralp Journal of Mathematics 8, no. 2 (October 2020): 376-83.
EndNote Sarıkaya MZ, Akkurt A, Budak H, Türkay ME, Yildirim H (October 1, 2020) On Some Special Functions for Conformable Fractional Integrals. Konuralp Journal of Mathematics 8 2 376–383.
IEEE M. Z. Sarıkaya, A. Akkurt, H. Budak, M. E. Türkay, and H. Yildirim, “On Some Special Functions for Conformable Fractional Integrals”, Konuralp J. Math., vol. 8, no. 2, pp. 376–383, 2020.
ISNAD Sarıkaya, Mehmet Zeki et al. “On Some Special Functions for Conformable Fractional Integrals”. Konuralp Journal of Mathematics 8/2 (October 2020), 376-383.
JAMA Sarıkaya MZ, Akkurt A, Budak H, Türkay ME, Yildirim H. On Some Special Functions for Conformable Fractional Integrals. Konuralp J. Math. 2020;8:376–383.
MLA Sarıkaya, Mehmet Zeki et al. “On Some Special Functions for Conformable Fractional Integrals”. Konuralp Journal of Mathematics, vol. 8, no. 2, 2020, pp. 376-83.
Vancouver Sarıkaya MZ, Akkurt A, Budak H, Türkay ME, Yildirim H. On Some Special Functions for Conformable Fractional Integrals. Konuralp J. Math. 2020;8(2):376-83.
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