본문 바로가기
KERD
논문KCI 등재

A study on Milne-type inequalities for a specific fractional integral operator with applications

Laxmi Rathour|Usman Ali|Ather Qayyum|Siti Suzlin Supadi|Arslan Munir|Gulnaz Atta
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2024.06|한국수학논문집 (Korean Journal of Mathematics)|제32권 제2호|pp. 297-314

0

조회

0

다운로드

1

인용

0

참고문헌

키워드

Fractional integrals$s$-convex functionHMilne-type inequalities"{o}lder's inequality
주제분류수학

초록

Fractional integral operators have been studied extensively in the last few decades by various mathematicians, because it plays a vital role in the developments of new inequalities. The main goal of the current study is to establish some new Milne-type inequalities by using the special type of fractional integral operator i.e Caputo Fabrizio operator. Additionally, generalization of these developed Milne-type inequalities for $s$-convex function are also given. Furthermore, applications to some special means, quadrature formula, and $q$-digamma functions are presented.

Abstract

Fractional integral operators have been studied extensively in the last few decades by various mathematicians, because it plays a vital role in the developments of new inequalities. The main goal of the current study is to establish some new Milne-type inequalities by using the special type of fractional integral operator i.e Caputo Fabrizio operator. Additionally, generalization of these developed Milne-type inequalities for $s$-convex function are also given. Furthermore, applications to some special means, quadrature formula, and $q$-digamma functions are presented.

참고문헌 (31)

  1. H. Sun, "A new collection of real world applications of fractional calculus in science and engineering", Commun. Nonlinear Sci. Numer. Simul, 64, pp.213~231 (2018)
  2. V. V. Kulish, "Application of fractional calculus to uid mechanics", J. Fluids Eng, 124, pp.803~806 (2002)[DOI]
  3. M. A. El-Shaed, "Fractional calculus model of the semilunar heart valve vibrations", International design engineering technical conferences and computers and information in engineering conference (2003)
  4. M. W. Alomari, "A companion of the generalized trapezoid inequality and applications", J. Math. Appl, 36, pp.5~15 (2013)
  5. S. S. Dragomir, "On trapezoid quadrature formula and applications", Kragujev. J. Math, 23, pp.25~36 (2001)
  6. M. Z. Sarikaya, "On the generalization of some integral inequalities and their applica-tions", Math. Comput. Model, 54, pp.2175~2182 (2011)[DOI]
  7. M. Z. Sarikaya, "Some Hermite-Hadamard type integral inequalities for twice dieren-tiable mappings via fractional integrals", Facta Univ., Ser. Math. Inform, 29(4), pp.371~384 (2014)
  8. U. S. Kirmaci, "Inequalities for dierentiable mappings and applications to special means of real numbers to midpoint formula", Appl. Math. Comput, 147(5), pp.137~146 (2004)[DOI]
  9. S. S. Dragomir, "On the midpoint quadrature formula for mappings with bounded variation and applications", Kragujev. J. Math, 22(13), pp.19~ (2000)
  10. M. Z. Sarikaya, "New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are convex and quasi-convex", Int. J. open probl. comput. sci. math, 5(3) (2012)[DOI]
  11. S. S. Dragomir, "On Simpson's inequality and applications", J. inequal. appl, 5, pp.533~579 (2000)
  12. M. Z. Sarikaya, "On new inequalities of Simpson's type for s-convex functions", Comput. math. appl, 60(8), pp.2191~2199 (2000)[DOI]
  13. T. Du, "A generalization of Simpson's inequality via dierentiable mapping using extended (s,m)-convex functions", Appl. math. comput, 293, pp.358~369 (2017)[DOI]
  14. S. S. Dragomir, "On Simpson's quadrature formula for mappings of bounded variation and appli-cations", Tamkang J. math, 30(1), pp.53~58 (1999)
  15. H. Yang, "New inequalities via Caputo-Fabrizio integral operator with applications", Aims Mathe, 8(8), pp.19391~19412 (2023)[DOI]
  16. N. A. Alqahtani., "Error bounds for fractional integral inequalities with applications", Fractal and Fractional, 8(4), pp.208~ (2024)[DOI]
  17. M. U. D. Junjua, "A study of some new Hermite-Hadamard inequalities via specic convex functions with applications", Mathematics, 12(3), pp.478~ (2024)[DOI]
  18. S. K. Paul, ", Analysis of mixed type nonlinear Volterra-Fredholm integral equations involving the Erdelyi-Kober fractional operator", Journal of king saud university-science, 35(10), pp.102949~ (2023)[DOI]
  19. V. K. Pathak, "On solvbility and approximatting the soultions for nonlinear innite system of frational functions integral equations in sequence space ℓp, p > 1", Journal of integral equations and applications, 35(4), pp.443~458 (2023)
  20. S. K. Paul, "Stability analysis through the Bielecki metric to nonlinear fractional integral equations of n-product operators", Aims Mathe, 9(4), pp.7770~7790 (2024)[DOI]
  21. V. K. Pathak, "On the solvability of a class of nonlinear functional integral equations involving Erdelyi-Kober fractional operator", Mathematical methods in the applied sciences, 46(13), pp.14340~14352 (2023)[DOI]
  22. S. K. Paul, "An eective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator", AIMS Mathematics, 8 (2023)[DOI]
  23. M. Raiz, "Approximation on bivariate of Durrmeyer operators based on beta function", The Journal of Analysis (2023)[DOI]
  24. M. Z. Sarikaya, "On new inequalities of simpson's type for s-convex functions", Comput. math. appl, 60, pp.2191~2199 (2010)[DOI]
  25. A. D. Booth, "Numerical Methods" (1966), Butterworths
  26. J. L. W. V. Jensen., "Surles fonctions convexes et les inegalites entre les valeurs moyennes", Acta math, 30, pp.175~193 (1905)
  27. H. Hudzik, "Some remarks on s-convex functions", Aequationes Math, 48, pp.100~111 (1994)
  28. S. Miller, "An Introduction to the Fractional Calculus and Fractional Dierential Equa-tions" (1993), Wiley
  29. H. Budak, "On new Milne-type inequalities for fractional integrals", J inequal appl, 10 (2023)[DOI]
  30. M. Caputo, "A new denition of fractional derivative without singular kernel", Progress in fractional dierentiation & applications, 1(2), pp.73~85 (2015)
  31. G. N. Watson, "A treatise on the theory of Bessel functions" (1955), Cambridge unversity press

관련 논문AI추천

A note on Simpson $3/8$ rule for function whose modulus of first derivatives are $s$-convex function with applicationArslan Munir, Hasan Kara, Huseyin Budak, Irza Faiz, Laxmi Rathour강원경기수학회 · 한국수학논문집2024 · 제32권 제3호Generalized Fractional Hermite Hadamard Type Inequalities for (s, m)-Convex Functions in the 1st and 2nd KindsAsif R. Khan, Muhammad Bilal한국수학교육학회 · 이론수학과 교직수학2025 · 제32권 제4호Some new estimates for exponentially $(\hbar,\mathfrak{m})$-convex functions via extended generalized fractional integral operatorsKhalida Inayat Noor, Muhammad Aslam Noor, Saima Rashid강원경기수학회 · 한국수학논문집2019 · 제27권 제4호$k-$fractional integral inequalities for $(h-m)-$convex functions via Caputo $k-$fractional derivativesAtiq Ur Rehman, Ghulam Farid, Lakshmi Narayan Mishra, Qurat Ul Ain강원경기수학회 · 한국수학논문집2019 · 제27권 제2호A new study on Simpson's type inequalities via generalized convexity with applicationAliya Fahmi, Ather Qayyum, Maimoona Karim, Siti Suzlin Supadi강원경기수학회 · 한국수학논문집2024 · 제32권 제4호Fractional versions of Hadamard inequalities for strongly $(s,m)$-convex functions via Caputo fractional derivativesGhulam Farid, Lakshmi Narayan Mishra, Laxmi Rathour, Sidra Bibi, Vishnu Narayan Mishra강원경기수학회 · 한국수학논문집2023 · 제31권 제1호

이 간행물의 다른 논문 (10건)

Fuzzy lattice ordered group based on fuzzy partial ordering relationSileshe Gone Korma, Parimi Radhakrishina Kishore, Dawit Chernet Kifetewpp. 195-211On the adapted partial differential equation for general diploid model of selection at a single locus최원pp. 213-218GENERALIZED α-KÖTHE TOEPLITZ DUALS OF CERTAIN DIFFERENCE SEQUENCE SPACESSandeep Gupta, Manoj Kumar, Ritupp. 219-228On the weakened hypotheses-based generalizations of the Enestr\"{o}m-Kakeya theoremShahbaz Mir, Abdul Limanpp. 229-243Expansive type mappings in dislocated quasi-metric space with some fixed point results and applicationHaripada Das, Nilakshi Goswamipp. 245-257
원문 보기