Research Article
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Year 2023, , 66 - 76, 31.07.2023
https://doi.org/10.54974/fcmathsci.1146523

Abstract

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.

Certain Weighted Fractional Integral Inequalities for Convex Functions

Year 2023, , 66 - 76, 31.07.2023
https://doi.org/10.54974/fcmathsci.1146523

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.

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.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Çetin Yıldız 0000-0002-8302-343X

Mustafa Gürbüz 0000-0002-7092-4298

Publication Date July 31, 2023
Published in Issue Year 2023

Cite

19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.