Research Article
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Year 2020, Volume: 5 Issue: 2, 140 - 146, 31.10.2020
https://izlik.org/JA62PR88NP

Abstract

References

  • 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

Year 2020, Volume: 5 Issue: 2, 140 - 146, 31.10.2020
https://izlik.org/JA62PR88NP

Abstract

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.

References

  • 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.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Saad Ihsan Butt

Mehroz Nadeem

Ghulam Farid

Publication Date October 31, 2020
IZ https://izlik.org/JA62PR88NP
Published in Issue Year 2020 Volume: 5 Issue: 2

Cite

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. https://izlik.org/JA62PR88NP
AMA 1.Butt SI, Nadeem M, Farid G. On Caputo Fractional Derivatives via Exponential s-Convex Functions. TJOS. 2020;5(2):140-146. https://izlik.org/JA62PR88NP
Chicago Butt, Saad Ihsan, Mehroz Nadeem, and Ghulam Farid. 2020. “On Caputo Fractional Derivatives via Exponential S-Convex Functions”. Turkish Journal of Science 5 (2): 140-46. https://izlik.org/JA62PR88NP.
EndNote Butt SI, Nadeem M, Farid G (October 1, 2020) On Caputo Fractional Derivatives via Exponential s-Convex Functions. Turkish Journal of Science 5 2 140–146.
IEEE [1]S. I. Butt, M. Nadeem, and G. Farid, “On Caputo Fractional Derivatives via Exponential s-Convex Functions”, TJOS, vol. 5, no. 2, pp. 140–146, Oct. 2020, [Online]. Available: https://izlik.org/JA62PR88NP
ISNAD Butt, Saad Ihsan - Nadeem, Mehroz - Farid, Ghulam. “On Caputo Fractional Derivatives via Exponential S-Convex Functions”. Turkish Journal of Science 5/2 (October 1, 2020): 140-146. https://izlik.org/JA62PR88NP.
JAMA 1.Butt SI, Nadeem M, Farid G. On Caputo Fractional Derivatives via Exponential s-Convex Functions. TJOS. 2020;5:140–146.
MLA Butt, Saad Ihsan, et al. “On Caputo Fractional Derivatives via Exponential S-Convex Functions”. Turkish Journal of Science, vol. 5, no. 2, Oct. 2020, pp. 140-6, https://izlik.org/JA62PR88NP.
Vancouver 1.Saad Ihsan Butt, Mehroz Nadeem, Ghulam Farid. On Caputo Fractional Derivatives via Exponential s-Convex Functions. TJOS [Internet]. 2020 Oct. 1;5(2):140-6. Available from: https://izlik.org/JA62PR88NP