Araştırma Makalesi
Yıl 2023,
Cilt: 6 Sayı: 2, 24 - 30, 30.12.2023
Öz
In this note, we have established some new integral inequalities
for product of two integrable functions by using Young inequality with a wellknown
classical inequality via Caputo-Fabrizio fractional integral operators.
Then, we have given some special cases of the main findings. The main results
have potential to usage in inequality theory.
Anahtar Kelimeler
Caputo-Fabrizio fractional integral operator Young inequality H¨older inequality.
Kaynakça
- 1. Abdeljawad, T., Baleanu, D. (2017). Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. J. Nonlinear Sci. Appl., 10, 1098–1107.
- 2. Abdeljawad, T., Baleanu, D. (2017). On fractional derivatives with exponential kernel and their discrete versions. Reports on Mathematical Physics, 80(1), 11-27.
- 3. Atangana, A., Baleanu, D. (2016). New fractional derivatives with non-local and non-singular kernel: Theory and Application to heat transfer model. Thermal Science, 20 (2), 763-769.
- 4. Tariq, M., Ahmad, H., Shaikh, A. G., Sahoo, S. K., Khedher, K. M., Gia, T. N. (2022). New fractional integral inequalities for preinvex functions involving Caputo Fabrizio operator. AIMS Mathematics,7(3):3440–3455.
- 5. Caputo, M., Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 73-85.
- 6. Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57-66.
- 7. Akdemir, A.O., Aslan, S., Çakaloğlu, M.N. and Set, E. New Hadamard Type Integral Inequalities via Caputo-Fabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (91) ICMRS 2021.
- 8. Akdemir, A., Aslan, S., Ekinci, A. (2022). Novel Approaches for s-Convex Functions via Caputo-Fabrizio Fractional integrals. Proceedings of IAM, 11(1), 3-16.
- 9. Akdemir, A.O., Aslan, S., Çakaloğlu, M.N. and Ekinci, A. Some New Results for Different Kinds of Convex Functions Caputo-Fabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (92) ICMRS 2021.
- 10. Akdemir, A. O., Butt, S. I., Nadeem, M., Ragusa, M. A. (2021). New general variants of Chebyshev type inequalities via generalized fractional integral operators. Mathematics, 9(2), 122. 11. Akdemir, A. O., Ekinci, A., Set, E. (2017). Conformable fractional integrals and related new integral inequalities, Journal of Nonlinear and Convex Analysis, 18 (4), 661-674.
- 12. Aslan, S. (2023). Some Novel Fractional Integral Inequalities for Different Kinds of Convex Functions. Eastern Anatolian Journal of Science, 9(1), 27-32.
- 13. Butt, S. I., Nadeem, M., Qaisar, S., Akdemir, A. O., Abdeljawad, T. (2020). Hermite–Jensen–Mercer type inequalities for conformable integrals and related results. Advances in Difference Equations, 2020(1), 1-24.
- 14. Butt, S. I., Umar, M., Rashid, S., Akdemir, A. O., Chu, Y. M. (2020). New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals. Advances in Difference Equations, 2020, 1-24.
- 15. Caputo, M., Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 73-85.
- 16. Ekinci, A., Özdemir, M.E. (2019). Some new integral inequalities via Riemann-Liouville integral operators. Applied and Computational Mathematics, 18(3), 288-295.
- 17. Rashid, S., Hammouch, Z., Kalsoom, H., Ashraf, R., Chu, Y. M. (2020). New investigation on the generalized k-fractional integral operators. Frontiers in Physics, 8, 25.
- 18. Rashid, S., Kalsoom, H., Hammouch, Z., Ashraf, R., Baleanu, D., Chu, Y. M. (2020). New multi-parametrized estimates having pth-order differentiability in fractional calculus for predominating ℏ-convex functions in Hilbert space. Symmetry, 12(2), 222.
- 19. Samko, S. G. (1993). Fractional integrals and derivatives. Theory and Applications, Gordon and Breach.
- 20. Set, E. (2012). New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Computers & Mathematics with Applications, 63(7), 1147-1154.
- 21. Set, E., Akdemir, A. O., Özdemir, E. M. (2017). Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat, 31(14), 4415-4420.
Yıl 2023,
Cilt: 6 Sayı: 2, 24 - 30, 30.12.2023
Öz
Kaynakça
- 1. Abdeljawad, T., Baleanu, D. (2017). Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. J. Nonlinear Sci. Appl., 10, 1098–1107.
- 2. Abdeljawad, T., Baleanu, D. (2017). On fractional derivatives with exponential kernel and their discrete versions. Reports on Mathematical Physics, 80(1), 11-27.
- 3. Atangana, A., Baleanu, D. (2016). New fractional derivatives with non-local and non-singular kernel: Theory and Application to heat transfer model. Thermal Science, 20 (2), 763-769.
- 4. Tariq, M., Ahmad, H., Shaikh, A. G., Sahoo, S. K., Khedher, K. M., Gia, T. N. (2022). New fractional integral inequalities for preinvex functions involving Caputo Fabrizio operator. AIMS Mathematics,7(3):3440–3455.
- 5. Caputo, M., Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 73-85.
- 6. Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57-66.
- 7. Akdemir, A.O., Aslan, S., Çakaloğlu, M.N. and Set, E. New Hadamard Type Integral Inequalities via Caputo-Fabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (91) ICMRS 2021.
- 8. Akdemir, A., Aslan, S., Ekinci, A. (2022). Novel Approaches for s-Convex Functions via Caputo-Fabrizio Fractional integrals. Proceedings of IAM, 11(1), 3-16.
- 9. Akdemir, A.O., Aslan, S., Çakaloğlu, M.N. and Ekinci, A. Some New Results for Different Kinds of Convex Functions Caputo-Fabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (92) ICMRS 2021.
- 10. Akdemir, A. O., Butt, S. I., Nadeem, M., Ragusa, M. A. (2021). New general variants of Chebyshev type inequalities via generalized fractional integral operators. Mathematics, 9(2), 122. 11. Akdemir, A. O., Ekinci, A., Set, E. (2017). Conformable fractional integrals and related new integral inequalities, Journal of Nonlinear and Convex Analysis, 18 (4), 661-674.
- 12. Aslan, S. (2023). Some Novel Fractional Integral Inequalities for Different Kinds of Convex Functions. Eastern Anatolian Journal of Science, 9(1), 27-32.
- 13. Butt, S. I., Nadeem, M., Qaisar, S., Akdemir, A. O., Abdeljawad, T. (2020). Hermite–Jensen–Mercer type inequalities for conformable integrals and related results. Advances in Difference Equations, 2020(1), 1-24.
- 14. Butt, S. I., Umar, M., Rashid, S., Akdemir, A. O., Chu, Y. M. (2020). New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals. Advances in Difference Equations, 2020, 1-24.
- 15. Caputo, M., Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 1(2), 73-85.
- 16. Ekinci, A., Özdemir, M.E. (2019). Some new integral inequalities via Riemann-Liouville integral operators. Applied and Computational Mathematics, 18(3), 288-295.
- 17. Rashid, S., Hammouch, Z., Kalsoom, H., Ashraf, R., Chu, Y. M. (2020). New investigation on the generalized k-fractional integral operators. Frontiers in Physics, 8, 25.
- 18. Rashid, S., Kalsoom, H., Hammouch, Z., Ashraf, R., Baleanu, D., Chu, Y. M. (2020). New multi-parametrized estimates having pth-order differentiability in fractional calculus for predominating ℏ-convex functions in Hilbert space. Symmetry, 12(2), 222.
- 19. Samko, S. G. (1993). Fractional integrals and derivatives. Theory and Applications, Gordon and Breach.
- 20. Set, E. (2012). New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Computers & Mathematics with Applications, 63(7), 1147-1154.
- 21. Set, E., Akdemir, A. O., Özdemir, E. M. (2017). Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat, 31(14), 4415-4420.
Toplam 20 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Operatör Cebirleri ve Fonksiyonel Analiz |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Aralık 2023 |
| Kabul Tarihi | 31 Ağustos 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 6 Sayı: 2 |
