Research Article
BibTex RIS Cite
Year 2023, Volume: 9 Issue: 1, 27 - 32, 30.06.2023

Abstract

References

  • ABDELJAWAD, THABET. On conformable fractional calculus. Journal of computational and Applied Mathematics, 2015, 279: 57-66.
  • ABDELJAWAD, THABET; BALEANU, DUMITRU. Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. arXiv preprint arXiv:1607.00262, 2016.
  • ABDELJAWAD, THABET; BALEANU, DUMITRU. On fractional derivatives with exponential kernel and their discrete versions. Reports on Mathematical Physics, 2017, 80.1: 11-27.
  • AKDEMİR, A. O.; ASLAN, S.; ÇAKALOĞLU, M.N. EKİNCİ, A. Some New Results for Different Kinds of Convex Functions CaputoFabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (92) ICMRS 2021.
  • AKDEMİR, A. O.; ASLAN, S.; ÇAKALOĞLU, M.N. SET, E. New Hadamard Type Integral Inequalities via Caputo-Fabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (91) ICMRS 2021.
  • AKDEMİR, A. O.; ASLAN, S.; EKİNCİ, A. Novel Approaches for s-Convex Functions via Caputo-Fabrizio Fractional Integrals. Proceedings of IAM, 2022, 11.1: 3-16.
  • AKDEMIR, AHMET OCAK, et al. New general variants of Chebyshev type inequalities via generalized fractional integral operators. Mathematics, 2021, 9.2: 122.
  • AKDEMIR, AHMET OCAK; EKINCI, ALPER; SET, ERHAN. Conformable fractional integrals and related new integral inequalities. 2017.
  • ATANGANA, ABDON; BALEANU, DUMITRU. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. arXiv preprint arXiv:1602.03408, 2016.
  • BRECKNER, WOLFGANG W. Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen. Publ. Inst. Math.(Beograd)(NS), 1978, 23.37: 13-20.
  • BUTT, SAAD IHSAN, et al. Hermite–Jensen–Mercer type inequalities for conformable integrals and related results. Advances in Difference Equations, 2020, 2020.1: 1-24.
  • BUTT, SAAD IHSAN, et al. New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals. Advances in Difference Equations, 2020, 2020: 1-24.
  • CAPUTO, MICHELE; FABRIZIO, MAURO. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 2015, 1.2: 73-85.
  • CAPUTO, MICHELE; FABRIZIO, MAURO. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 2015, 1.2: 73-85.
  • EKINCI, ALPER; OZDEMIR, MUHAMET. Some new integral inequalities via Riemann-Liouville integral operators. Applied and computational mathematics, 2019, 18.3.
  • GÜRBÜZ, MUSTAFA, et al. Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities. Journal of Inequalities and Applications, 2020, 2020: 1-10.
  • PEAJCARIAAC, JOSIP E.; TONG, YUNG LIANG. Convex functions, partial orderings, and statistical applications. Academic Press, 1992.
  • RASHID, SAIMA, et al. New investigation on the generalized K-fractional integral operators. Frontiers in Physics, 2020, 8: 25.
  • RASHID, SAIMA, et al. New multi-parametrized estimates having pth-order differentiability in fractional calculus for predominating ℏ-convex functions in Hilbert space. Symmetry, 2020, 12.2: 222.
  • SAMKO, STEFAN G., et al. Fractional integrals and derivatives. Yverdon-les-Bains, Switzerland: Gordon and breach science publishers, Yverdon, 1993.
  • SET, ERHAN. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Computers & Mathematics with Applications, 2012, 63.7: 1147-1154.
  • SET, ERHAN. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Computers & Mathematics with Applications, 2012, 63.7: 1147-1154.
  • SET, ERHAN; AKDEMIR, AHMET OCAK; ÖZDEMIR, Emin M. Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat, 2017, 31.14: 4415-4420.
  • TARIQ, MUHAMMAD, et al. New fractional integral inequalities for preinvex functions involving caputo fabrizio operator. 2022.
  • VAROŠANEC, SANJA. On h-convexity. Journal of Mathematical Analysis and Applications, 2007, 326.1: 303-311.DAVIS, S., MIRICK, D.K., STEVENS, R.G. (2002). Residential magnetic fields and the risk of breast cancer, Am J Epidemiol,155 (5), 446 – 454.

SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS

Year 2023, Volume: 9 Issue: 1, 27 - 32, 30.06.2023

Abstract

In this paper, some novel integral inequalities for different kinds of
convex functions have been proved by using Caputo-Fabrizio fractional integral
operators. The findings includes several new integral inequalities h-convex
functions, s-convex functions in the second sense. We have used the properties
of Caputo-Fabrizio fractional operator, definition of different kinds of convex
functions and elemantery analysis methods.

References

  • ABDELJAWAD, THABET. On conformable fractional calculus. Journal of computational and Applied Mathematics, 2015, 279: 57-66.
  • ABDELJAWAD, THABET; BALEANU, DUMITRU. Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. arXiv preprint arXiv:1607.00262, 2016.
  • ABDELJAWAD, THABET; BALEANU, DUMITRU. On fractional derivatives with exponential kernel and their discrete versions. Reports on Mathematical Physics, 2017, 80.1: 11-27.
  • AKDEMİR, A. O.; ASLAN, S.; ÇAKALOĞLU, M.N. EKİNCİ, A. Some New Results for Different Kinds of Convex Functions CaputoFabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (92) ICMRS 2021.
  • AKDEMİR, A. O.; ASLAN, S.; ÇAKALOĞLU, M.N. SET, E. New Hadamard Type Integral Inequalities via Caputo-Fabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (91) ICMRS 2021.
  • AKDEMİR, A. O.; ASLAN, S.; EKİNCİ, A. Novel Approaches for s-Convex Functions via Caputo-Fabrizio Fractional Integrals. Proceedings of IAM, 2022, 11.1: 3-16.
  • AKDEMIR, AHMET OCAK, et al. New general variants of Chebyshev type inequalities via generalized fractional integral operators. Mathematics, 2021, 9.2: 122.
  • AKDEMIR, AHMET OCAK; EKINCI, ALPER; SET, ERHAN. Conformable fractional integrals and related new integral inequalities. 2017.
  • ATANGANA, ABDON; BALEANU, DUMITRU. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. arXiv preprint arXiv:1602.03408, 2016.
  • BRECKNER, WOLFGANG W. Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen. Publ. Inst. Math.(Beograd)(NS), 1978, 23.37: 13-20.
  • BUTT, SAAD IHSAN, et al. Hermite–Jensen–Mercer type inequalities for conformable integrals and related results. Advances in Difference Equations, 2020, 2020.1: 1-24.
  • BUTT, SAAD IHSAN, et al. New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals. Advances in Difference Equations, 2020, 2020: 1-24.
  • CAPUTO, MICHELE; FABRIZIO, MAURO. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 2015, 1.2: 73-85.
  • CAPUTO, MICHELE; FABRIZIO, MAURO. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 2015, 1.2: 73-85.
  • EKINCI, ALPER; OZDEMIR, MUHAMET. Some new integral inequalities via Riemann-Liouville integral operators. Applied and computational mathematics, 2019, 18.3.
  • GÜRBÜZ, MUSTAFA, et al. Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities. Journal of Inequalities and Applications, 2020, 2020: 1-10.
  • PEAJCARIAAC, JOSIP E.; TONG, YUNG LIANG. Convex functions, partial orderings, and statistical applications. Academic Press, 1992.
  • RASHID, SAIMA, et al. New investigation on the generalized K-fractional integral operators. Frontiers in Physics, 2020, 8: 25.
  • RASHID, SAIMA, et al. New multi-parametrized estimates having pth-order differentiability in fractional calculus for predominating ℏ-convex functions in Hilbert space. Symmetry, 2020, 12.2: 222.
  • SAMKO, STEFAN G., et al. Fractional integrals and derivatives. Yverdon-les-Bains, Switzerland: Gordon and breach science publishers, Yverdon, 1993.
  • SET, ERHAN. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Computers & Mathematics with Applications, 2012, 63.7: 1147-1154.
  • SET, ERHAN. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Computers & Mathematics with Applications, 2012, 63.7: 1147-1154.
  • SET, ERHAN; AKDEMIR, AHMET OCAK; ÖZDEMIR, Emin M. Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat, 2017, 31.14: 4415-4420.
  • TARIQ, MUHAMMAD, et al. New fractional integral inequalities for preinvex functions involving caputo fabrizio operator. 2022.
  • VAROŠANEC, SANJA. On h-convexity. Journal of Mathematical Analysis and Applications, 2007, 326.1: 303-311.DAVIS, S., MIRICK, D.K., STEVENS, R.G. (2002). Residential magnetic fields and the risk of breast cancer, Am J Epidemiol,155 (5), 446 – 454.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Methods and Special Functions
Journal Section makaleler
Authors

Sinan Aslan 0000-0001-5970-1926

Publication Date June 30, 2023
Published in Issue Year 2023 Volume: 9 Issue: 1

Cite

APA Aslan, S. (2023). SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS. Eastern Anatolian Journal of Science, 9(1), 27-32.
AMA Aslan S. SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS. Eastern Anatolian Journal of Science. June 2023;9(1):27-32.
Chicago Aslan, Sinan. “SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS”. Eastern Anatolian Journal of Science 9, no. 1 (June 2023): 27-32.
EndNote Aslan S (June 1, 2023) SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS. Eastern Anatolian Journal of Science 9 1 27–32.
IEEE S. Aslan, “SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS”, Eastern Anatolian Journal of Science, vol. 9, no. 1, pp. 27–32, 2023.
ISNAD Aslan, Sinan. “SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS”. Eastern Anatolian Journal of Science 9/1 (June 2023), 27-32.
JAMA Aslan S. SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS. Eastern Anatolian Journal of Science. 2023;9:27–32.
MLA Aslan, Sinan. “SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS”. Eastern Anatolian Journal of Science, vol. 9, no. 1, 2023, pp. 27-32.
Vancouver Aslan S. SOME NOVEL FRACTIONAL INTEGRAL INEQUALITIES FOR DIFFERENT KINDS OF CONVEX FUNCTIONS. Eastern Anatolian Journal of Science. 2023;9(1):27-32.