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 Volume V Issue II 2020
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 (Ekim 2020), 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.