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Year 2020, Volume: 69 Issue: 1, 37 - 48, 30.06.2020
https://doi.org/10.31801/cfsuasmas.484437

Abstract

References

  • Chen, H. and Katugampola, U. N., Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for generalized fractional integrals, J. Math. Anal. Appl., 446 (2017), 1274-1291.
  • Diaza, R. and Pariglan, E., On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 15(2) (2007), 179--192.
  • Dragomir, S. S., Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11(5) (1998), 91--95.
  • Farid, G., Some Riemann-Liouville fractional integral inequalities for convex functions, J. Anal., (2018), doi.org/10.1007/s41478-0079-4.
  • Farid, G., Rehman, A. U., and Zahra, M., On Hadamard inequalities for k-fractional integrals, Nonlinear Funct. Anal. Appl., 21(3) (2016), 463--478.
  • Habib, S., Mubeen, S., and Naeem, M. N., Chebyshev type integral inequalities for generalized k-fractional conformable integrals, J. Inequal. Spec. Funct., 9(4) (2018), 53-65.
  • arad, F., Ugurlu, E., Abdeljawad, T., and Baleanu, D., On a new class of fractional operators, Adv. Difference Equ., (2017), 2017:247.
  • Khan, T. U., and Khan, M. A., Generalized conformable fractional operators, J. Comput. Appl. Math., 346 (2019), 378--389.
  • Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J., Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier, New York-London, 2006.
  • Kwun, Y. C., Farid, G., Nazeer, W., Ullah, S., Kang, S. M., Generalized Riemann-Liouville k-fractional integrals associated with Ostrowski type inequalities and error bounds of Hadamard inequalities, IEEE Access, 6 (2018), 64946--64953. S. S. Dragomir, Th. M. Rassias (Eds.), Kluwer academic publishers, Dordrecht, Boston, London (2002).
  • Lazarević, M., Advanced topics on applications of fractional calculus on control problems, System stability and modeling, WSEAS Press, 2014.
  • Letnikov, A. V., Theory of differentiation with an arbitrary index (Russian), Moscow, Matem. Sbornik, 3 (1868), 1--66.
  • Samko, S. G., Kilbas, A. A., and Marichev, O. I., Fractional integrals and derivatives: Theory and Applications, Gordon and Breach Science Publishers, 1993.
  • Roberts, A. W., Varberg, D. E., Convex functions, Academic Press, New York, 1973.
  • Sabatier, J., Agrawal, O. P., and J. T. Machado, Advances in fractional calculus: Theoretical developments and applications in Physics and Engineering, Springer 2007.
  • Sarikaya, M. Z., Dahmani, M., Kiris, M. E., and Ahmad, F., (k, s)-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat., 45(1) (2016), 77--89.
  • NY : Sonin, N. Y., On differentiation with arbitray index, Moscow Matem. Sbornik, 6(1) (1869), 1--38.

Study of a generalized Riemann-Liouville fractional integral via convex functions

Year 2020, Volume: 69 Issue: 1, 37 - 48, 30.06.2020
https://doi.org/10.31801/cfsuasmas.484437

Abstract

 In this paper estimations in general form of sum of left and right sided Riemann-Liouville (RL) fractional integrals for convex functions are studied. Also some similar fractional inequalities for functions whose derivatives in absolute value are convex, have been obtained. Associated fractional integral inequalities provide the bounds of different known fractional inequalities. These results may be useful in in the study of uniqueness solutions of fractional differential equations and fractional boundary value problems.

References

  • Chen, H. and Katugampola, U. N., Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for generalized fractional integrals, J. Math. Anal. Appl., 446 (2017), 1274-1291.
  • Diaza, R. and Pariglan, E., On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 15(2) (2007), 179--192.
  • Dragomir, S. S., Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11(5) (1998), 91--95.
  • Farid, G., Some Riemann-Liouville fractional integral inequalities for convex functions, J. Anal., (2018), doi.org/10.1007/s41478-0079-4.
  • Farid, G., Rehman, A. U., and Zahra, M., On Hadamard inequalities for k-fractional integrals, Nonlinear Funct. Anal. Appl., 21(3) (2016), 463--478.
  • Habib, S., Mubeen, S., and Naeem, M. N., Chebyshev type integral inequalities for generalized k-fractional conformable integrals, J. Inequal. Spec. Funct., 9(4) (2018), 53-65.
  • arad, F., Ugurlu, E., Abdeljawad, T., and Baleanu, D., On a new class of fractional operators, Adv. Difference Equ., (2017), 2017:247.
  • Khan, T. U., and Khan, M. A., Generalized conformable fractional operators, J. Comput. Appl. Math., 346 (2019), 378--389.
  • Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J., Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier, New York-London, 2006.
  • Kwun, Y. C., Farid, G., Nazeer, W., Ullah, S., Kang, S. M., Generalized Riemann-Liouville k-fractional integrals associated with Ostrowski type inequalities and error bounds of Hadamard inequalities, IEEE Access, 6 (2018), 64946--64953. S. S. Dragomir, Th. M. Rassias (Eds.), Kluwer academic publishers, Dordrecht, Boston, London (2002).
  • Lazarević, M., Advanced topics on applications of fractional calculus on control problems, System stability and modeling, WSEAS Press, 2014.
  • Letnikov, A. V., Theory of differentiation with an arbitrary index (Russian), Moscow, Matem. Sbornik, 3 (1868), 1--66.
  • Samko, S. G., Kilbas, A. A., and Marichev, O. I., Fractional integrals and derivatives: Theory and Applications, Gordon and Breach Science Publishers, 1993.
  • Roberts, A. W., Varberg, D. E., Convex functions, Academic Press, New York, 1973.
  • Sabatier, J., Agrawal, O. P., and J. T. Machado, Advances in fractional calculus: Theoretical developments and applications in Physics and Engineering, Springer 2007.
  • Sarikaya, M. Z., Dahmani, M., Kiris, M. E., and Ahmad, F., (k, s)-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat., 45(1) (2016), 77--89.
  • NY : Sonin, N. Y., On differentiation with arbitray index, Moscow Matem. Sbornik, 6(1) (1869), 1--38.
There are 17 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Ghulam Farid 0000-0002-4103-7745

Publication Date June 30, 2020
Submission Date November 16, 2018
Acceptance Date July 9, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Farid, G. (2020). Study of a generalized Riemann-Liouville fractional integral via convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 37-48. https://doi.org/10.31801/cfsuasmas.484437
AMA Farid G. Study of a generalized Riemann-Liouville fractional integral via convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):37-48. doi:10.31801/cfsuasmas.484437
Chicago Farid, Ghulam. “Study of a Generalized Riemann-Liouville Fractional Integral via Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 37-48. https://doi.org/10.31801/cfsuasmas.484437.
EndNote Farid G (June 1, 2020) Study of a generalized Riemann-Liouville fractional integral via convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 37–48.
IEEE G. Farid, “Study of a generalized Riemann-Liouville fractional integral via convex functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 37–48, 2020, doi: 10.31801/cfsuasmas.484437.
ISNAD Farid, Ghulam. “Study of a Generalized Riemann-Liouville Fractional Integral via Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 37-48. https://doi.org/10.31801/cfsuasmas.484437.
JAMA Farid G. Study of a generalized Riemann-Liouville fractional integral via convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:37–48.
MLA Farid, Ghulam. “Study of a Generalized Riemann-Liouville Fractional Integral via Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 37-48, doi:10.31801/cfsuasmas.484437.
Vancouver Farid G. Study of a generalized Riemann-Liouville fractional integral via convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):37-48.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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