On Caputo Fractional Derivatives via Exponential s-Convex Functions

Year 2020, Volume: 5 Issue: 2, 140 - 146, 31.10.2020

Saad Ihsan Butt , Mehroz Nadeem , Ghulam Farid

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.

Keywords

convex function , exponential s-convex functions , Caputo-Fractional derivatives

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.