Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2020, Cilt: 5 Sayı: 2, 140 - 146, 31.10.2020

Öz

Kaynakça

  • A. A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and applications of Fractional Differential Equations,North-Holland Mathematics Studies, Elsevier, New York-London, 2006.
  • C. P. Li and W. H. Deng, Remarks on fractional derivatives, Appl. Math. Comput., 187(2) (2007), 777-784.
  • G. Farid, S. Naqvi and A. U. Rehman, A version of the Hadamard inequality for Caputo fractional derivatives and related results, RGMIA Research Report Collection, 20 (2017).
  • G. Farid,On Caputo Fractional Derivatives Via Convexity,Kragujevac Journal Of Mthematics, 44(3),(2020), 393-399.
  • G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities,Cambridge, UK : Cambridge University Press, Cambridge mathematical library, 1952.
  • H.Hudzik, L. Maligranda,Some remarks on s-convex functions,Aequ. Math. 48(1), 1994, 100-111.
  • L. N. Mishra, Q. U. Ain, G. Farid and A. U. Rehman, k−fractional integral inequalities for (h,m)− convex functions via Caputo k− fractional derivatives, The Korean Journal of Mathematics, 27(2), (2019), 357-374.
  • M. Caputo,Linear model of dissipation whose Q is almost frequency independent Geophysical Journal International, 13(5), 1967, 529-539.
  • M.U. Awan, M.A. Noor, K.I. Noor,Hermite-Hadamard inequalities for exponentially convex functions,Appl. Math. Inf. Sci. 12(2), 2018, 405-409.
  • N. Mehreen, M. Anwar,Hermite-Hadamard type inequalities fo exponentially p-convex functions and exponentialli sconvex functions in the second sense with applications,J Inequal. Appl. 92, 2019.
  • S. Naqvi, G. Farid and B. Tariq, Caputo fractional integral inequalities via m convex function,RGMIA Research Report Collection, (2014).
  • S. Miller, B. Ross,An introduction to fractional calculus and fractional differential equations,John Wiley And Sons, Usa., (2), 1993.

On Caputo Fractional Derivatives via Exponential s-Convex Functions

Yıl 2020, Cilt: 5 Sayı: 2, 140 - 146, 31.10.2020

Öz

In this paper, we establish several new integral inequalities including Caputo fractional integrals for exponential s-convex functions. By using convexity for exponential s-convex functions of any integer order differentiable function some novel results are given.

In this paper, we establish several new integral inequalities including Caputo fractional integrals for exponential s-convex functions. By using convexity for exponential s-convex functions of any integer order differentiable function some novel results are given.

Kaynakça

  • A. A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and applications of Fractional Differential Equations,North-Holland Mathematics Studies, Elsevier, New York-London, 2006.
  • C. P. Li and W. H. Deng, Remarks on fractional derivatives, Appl. Math. Comput., 187(2) (2007), 777-784.
  • G. Farid, S. Naqvi and A. U. Rehman, A version of the Hadamard inequality for Caputo fractional derivatives and related results, RGMIA Research Report Collection, 20 (2017).
  • G. Farid,On Caputo Fractional Derivatives Via Convexity,Kragujevac Journal Of Mthematics, 44(3),(2020), 393-399.
  • G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities,Cambridge, UK : Cambridge University Press, Cambridge mathematical library, 1952.
  • H.Hudzik, L. Maligranda,Some remarks on s-convex functions,Aequ. Math. 48(1), 1994, 100-111.
  • L. N. Mishra, Q. U. Ain, G. Farid and A. U. Rehman, k−fractional integral inequalities for (h,m)− convex functions via Caputo k− fractional derivatives, The Korean Journal of Mathematics, 27(2), (2019), 357-374.
  • M. Caputo,Linear model of dissipation whose Q is almost frequency independent Geophysical Journal International, 13(5), 1967, 529-539.
  • M.U. Awan, M.A. Noor, K.I. Noor,Hermite-Hadamard inequalities for exponentially convex functions,Appl. Math. Inf. Sci. 12(2), 2018, 405-409.
  • N. Mehreen, M. Anwar,Hermite-Hadamard type inequalities fo exponentially p-convex functions and exponentialli sconvex functions in the second sense with applications,J Inequal. Appl. 92, 2019.
  • S. Naqvi, G. Farid and B. Tariq, Caputo fractional integral inequalities via m convex function,RGMIA Research Report Collection, (2014).
  • S. Miller, B. Ross,An introduction to fractional calculus and fractional differential equations,John Wiley And Sons, Usa., (2), 1993.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Saad Ihsan Butt

Mehroz Nadeem

Ghulam Farid

Yayımlanma Tarihi 31 Ekim 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 5 Sayı: 2

Kaynak Göster

APA Butt, S. I., Nadeem, M., & Farid, G. (2020). On Caputo Fractional Derivatives via Exponential s-Convex Functions. Turkish Journal of Science, 5(2), 140-146.
AMA Butt SI, Nadeem M, Farid G. On Caputo Fractional Derivatives via Exponential s-Convex Functions. TJOS. Ekim 2020;5(2):140-146.
Chicago Butt, Saad Ihsan, Mehroz Nadeem, ve Ghulam Farid. “On Caputo Fractional Derivatives via Exponential s-Convex Functions”. Turkish Journal of Science 5, sy. 2 (Ekim 2020): 140-46.
EndNote Butt SI, Nadeem M, Farid G (01 Ekim 2020) On Caputo Fractional Derivatives via Exponential s-Convex Functions. Turkish Journal of Science 5 2 140–146.
IEEE S. I. Butt, M. Nadeem, ve G. Farid, “On Caputo Fractional Derivatives via Exponential s-Convex Functions”, TJOS, c. 5, sy. 2, ss. 140–146, 2020.
ISNAD Butt, Saad Ihsan vd. “On Caputo Fractional Derivatives via Exponential s-Convex Functions”. Turkish Journal of Science 5/2 (Ekim2020), 140-146.
JAMA Butt SI, Nadeem M, Farid G. On Caputo Fractional Derivatives via Exponential s-Convex Functions. TJOS. 2020;5:140–146.
MLA Butt, Saad Ihsan vd. “On Caputo Fractional Derivatives via Exponential s-Convex Functions”. Turkish Journal of Science, c. 5, sy. 2, 2020, ss. 140-6.
Vancouver Butt SI, Nadeem M, Farid G. On Caputo Fractional Derivatives via Exponential s-Convex Functions. TJOS. 2020;5(2):140-6.