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On Some Special Functions for Conformable Fractional Integrals

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

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.                                                                                                                                                                                                                                                      

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.

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

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.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Mehmet Zeki SARIKAYA
DÜZCE ÜNİVERSİTESİ
Türkiye


Abdullah AKKURT
KAHRAMANMARAŞ SÜTÇÜ İMAM ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ
0000-0001-5644-1276
Türkiye


Hüseyin BUDAK (Primary Author)
DUZCE UNIVERSITY
Türkiye


Merve Esra TÜRKAY
CUMHURIYET UNIVERSITY, FACULTY OF SCIENCE
0000-0003-4429-2685
Türkiye


Hüseyin YİLDİRİM
KAHRAMANMARAŞ SÜTÇÜ İMAM ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ
0000-0001-8855-9260
Türkiye

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

Cite

Bibtex @research article { konuralpjournalmath810524, journal = {Konuralp Journal of Mathematics (KJM)}, issn = {}, eissn = {2147-625X}, address = {}, publisher = {Mehmet Zeki SARIKAYA}, year = {2020}, volume = {8}, pages = {376 - 383}, doi = {}, title = {On Some Special Functions for Conformable Fractional Integrals}, key = {cite}, author = {Sarıkaya, Mehmet Zeki and Akkurt, Abdullah and Budak, Hüseyin and Türkay, Merve Esra and Yildirim, Hüseyin} }
APA Sarıkaya, M. Z. , Akkurt, A. , Budak, H. , Türkay, M. E. & Yildirim, H. (2020). On Some Special Functions for Conformable Fractional Integrals . Konuralp Journal of Mathematics (KJM) , 8 (2) , 376-383 . Retrieved from https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/31495/810524
MLA Sarıkaya, M. Z. , Akkurt, A. , Budak, H. , Türkay, M. E. , Yildirim, H. "On Some Special Functions for Conformable Fractional Integrals" . Konuralp Journal of Mathematics (KJM) 8 (2020 ): 376-383 <https://dergipark.org.tr/en/pub/konuralpjournalmath/issue/31495/810524>
Chicago Sarıkaya, M. Z. , Akkurt, A. , Budak, H. , Türkay, M. E. , Yildirim, H. "On Some Special Functions for Conformable Fractional Integrals". Konuralp Journal of Mathematics (KJM) 8 (2020 ): 376-383
RIS TY - JOUR T1 - On Some Special Functions for Conformable Fractional Integrals AU - Mehmet Zeki Sarıkaya , Abdullah Akkurt , Hüseyin Budak , Merve Esra Türkay , Hüseyin Yildirim Y1 - 2020 PY - 2020 N1 - DO - T2 - Konuralp Journal of Mathematics (KJM) JF - Journal JO - JOR SP - 376 EP - 383 VL - 8 IS - 2 SN - -2147-625X M3 - UR - Y2 - 2020 ER -
EndNote %0 Konuralp Journal of Mathematics (KJM) On Some Special Functions for Conformable Fractional Integrals %A Mehmet Zeki Sarıkaya , Abdullah Akkurt , Hüseyin Budak , Merve Esra Türkay , Hüseyin Yildirim %T On Some Special Functions for Conformable Fractional Integrals %D 2020 %J Konuralp Journal of Mathematics (KJM) %P -2147-625X %V 8 %N 2 %R %U
ISNAD Sarıkaya, Mehmet Zeki , Akkurt, Abdullah , Budak, Hüseyin , Türkay, Merve Esra , Yildirim, Hüseyin . "On Some Special Functions for Conformable Fractional Integrals". Konuralp Journal of Mathematics (KJM) 8 / 2 (October 2020): 376-383 .
AMA Sarıkaya M. Z. , Akkurt A. , Budak H. , Türkay M. E. , Yildirim H. On Some Special Functions for Conformable Fractional Integrals. Konuralp J. Math.. 2020; 8(2): 376-383.
Vancouver Sarıkaya M. Z. , Akkurt A. , Budak H. , Türkay M. E. , Yildirim H. On Some Special Functions for Conformable Fractional Integrals. Konuralp Journal of Mathematics (KJM). 2020; 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 Journal of Mathematics (KJM), vol. 8, no. 2, pp. 376-383, Oct. 2020
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