Certain Weighted Fractional Integral Inequalities for Convex Functions

Year 2023, Volume: 4 Issue: 2 , 66 - 76 , 31.07.2023

Çetin Yıldız , Mustafa Gürbüz

https://doi.org/10.54974/fcmathsci.1146523

https://izlik.org/JA79RG68UG

Abstract

In this study, by using the monotonicity properties of functions, several inequalities for convex functions are obtained with the help of a weighted fractional integral operator which provides a function f to be integrated in fractional order with respect to another function. It is also seen that the results obtained were generalizations of the previous results presented.

Keywords

Convex functions , Weighted fractional operators , Fractional integral inequality.

References

• Liu W.J., Ngo Q.A., Huy V.N., Several interesting integral inequalities, Journal of Mathematical Inequalities, 3, 201-212, 2009.
• Mitrinović D.S., Pečarić J.E., Fink A.M., Classical and New Inequalities in Analysis, Kluwer Academic Publishers, 1993.
• Jarad F., Abdeljawad T., Shah K., On the weighted fractional operators of a function with respect to another function, Fractals, 28(08), 20040011, 2020.
• Osler T.J., The fractional derivative of a composite function, SIAM Journal on Mathematical Analysis, 1, 288-293, 1970.
• Almeira R., A Caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation, 44, 460-481, 2017.
• Kilbas A.A., Hadamard-type fractional calculus, Journal of the Korean Mathematical Society, 38, 1191-1204, 2001.
• Ngo Q.A., Thang D.D., Dat T.T., Tuan D.A., Notes on an integral inequality, Journal of Inequalities in Pure and Applied Mathematics, 7(4), 120, 2006.
• Liu W.J., Cheng G.S., Li C.C., Further development of an open problem concerning an integral inequality, Journal of Inequalities in Pure and Applied Mathematics, 9(1), 14, 2008.
• Dahmani Z., A note on some new fractional results involving convex functions, Acta Mathematica Universitatis Comenianae, LXXXI, 241-246, 2012.
• Rahman G., Nisar K.S., Abdeljawad T., Ullah S., Certain fractional proportional integral inequalities via convex functions, Mathematics, 8, 222, 2020.
• Rahman G., Nisar K.S., Abdeljawad T., Tempered fractional integral inequalities for convex functions, Mathematics, 8(4), 500, 2020.
• Rahman G., Abdeljawad T., Jarad F., Khan A., Nisar K.S., Certain inequalities via generalized proportional Hadamard fractional integral operators, Advances in Differential Equations, 2019:454, 2019.