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On Opial-type inequality for a generalized fractional integral operator

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Języki publikacji
EN
Abstrakty
EN
This article is aimed at establishing some results concerning integral inequalities of the Opial type in the fractional calculus scenario. Specifically, a generalized definition of a fractional integral operator is introduced from a new Raina-type special function, and with certain results proposed in previous publications and the choice of the parameters involved, the established results in the work are obtained. In addition, some criteria are established to obtain the aforementioned inequalities based on other integral operators. Finally, a more generalized definition is suggested, with which interesting results can be obtained in the field of fractional integral inequalities.
Wydawca
Rocznik
Strony
695--709
Opis fizyczny
Bibliogr. 41 poz.
Twórcy
  • Pontificia Universidad Católica del Ecuador, Facultad de Ciencias Naturales y Exactas, Escuela de Ciencias Físicas y Matemáticas, Av. 12 de Octubre 1076. Apartado, Quito 17-01-2184, Ecuador
  • Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, España
  • Universidad Nacional del Nordeste, Facultad de Ciencias Exactas y Naturales y Agrimensura, Corrientes, Argentina
  • Departamento de Técnicas Cuantitativas, Universidad Centroccidental Lisandro Alvarado, Decanato de Ciencias Económicas y Empresariales, Barquisimeto, Venezuela
Bibliografia
  • [1] D. Baleanu, P. O. Mohammed, M. Vivas-Cortez, and Y. Rangel-Oliveros, Some modifications in conformable fractional integral inequalities, Adv. Differ. Equ. 2020 (2020), no. 1, 374–380, DOI: https://doi.org/10.1186/s13662-020-02837-0.
  • [2] T. Abdeljawad, P. O. Mohammed, and A. Kashuri, New modified conformable fractional integral inequalities of Hermite-Hadamard type with applications, J. Funct. Space 2020 (2020), no. 1, 357–435, DOI: https://doi.org/10.1155/2020/4352357.
  • [3] P. O. Mohammed, Some integral inequalities of fractional quantum type, Malaya J. Mat. 4 (2016), no. 1, 93–99.
  • [4] P. O. Mohammed and T. Abdeljawad, Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel, Adv. Differ. Equ. 2020 (2020), no. 1, 345–363, DOI: https://doi.org/10.1186/s13662-020-02825-4.
  • [5] O. Bazighifan, An approach for studying asymptotic properties of solutions of neutral differential equations, Symmetry 12 (2020), no. 4, 1–20, DOI: https://doi.org/10.3390/sym12040555.
  • [6] P. O. Mohammed and M. Z. Sarikaya, On generalized fractional integral inequalities for twice differentiable convex functions, J. Comput. Appl. Math. 372 (2020), no. 1, 1–15, DOI: https://doi.org/10.1016/j.cam.2020.112740.
  • [7] M. J. Cloud, B. C. Drachman, and L. Lebedev, Inequalities with Applications to Engineering, Springer International Publishing, New York, 2014.
  • [8] I. Ahmad, H. Ahmad, P. Thounthong, Y.-M. Chu, and C. Cesarano, Solution of multi-term time-fractional PDE models arising in mathematical biology and physics by local meshless method, Symmetry 12 (2020), no. 7, 1–20, DOI: https://doi.org/10.3390/sym12071195.
  • [9] F. M. Atici and H. Yaldiz, Convex functions on discrete time domains, Canad. Math. Bull. 59 (2016), no. 1, 225–233, DOI: https://doi.org/10.4153/CMB-2015-065-6.
  • [10] R. P. Agarwal, P. Y. M. Pang, Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Academic Publishers, London, 1995
  • [11] D. S. Mitrinovic, J. E. Pećarić, and A. M. Fink, Opial’s inequality, in: Inequalities Involving Functions and Their Integrals and Derivatives: Mathematics and Its Applications, East European Series, vol. 53, Springer, Dordrecht, 1991.
  • [12] J. Calvert, Some generalizations of Opial’s inequality, Proc. Amer. Math. Soc. 18 (1967), no. 1, 72–75, DOI: https://doi.org/10.1090/s0002-9939-1967-0204594-1.
  • [13] C.-J. Zhao, On Opial’s type integral inequalities, Mathematics 7 (2019), no. 4, 375, 1–9, DOI: https://doi.org/10.3390/math7040375.
  • [14] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley & Sons, New York, 1993.
  • [15] G. Farid, A. U. Rehman, and S. Ullah, Opial-type inequalities for convex functions and associated results in fractional calculus, Adv. Differ. Equ. 152 (2019), no. 1, 1–13, DOI: https://doi.org/10.1186/s13662-019-2089-1.
  • [16] Z. Opial, Sur une inegalite, Ann. Polon. Math. 8 (1960), no. 1, 29–32.
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  • [22] A. Atangana, Fractional Operators with Constant and Variable Order with Application to Geo-hydrology, Academic Press, New York, 2017.
  • [23] J. Hristov, The Craft of Fractional Modelling in Science and Engineering, MDPI, Basel, 2018.
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  • [26] T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J. 19 (1971), no. 1, 7–15.
  • [27] T. O. Salim and A. W. Faraj, A generalization of Mittag-Leffler function and integral operator associated with fractional calculus, J. Fract. Calc. Appl. 3 (2012), no. 5, 1–13.
  • [28] R. K. Raina, On generalized Wright’s hypergeometric functions and fractional calculus operator, East Asian Math. J. 21 (2005), no. 2, 191–203.
  • [29] R. P. Agarwal, M.-J. Luo, and R. K. Raina, On Ostrowski type inequalities, Fasc. Math. 56 (2016), no. 1, 5–27, DOI: https://doi.org/10.1515/fascmath-2016-0001.
  • [30] S.-B. Chen, S. Rashid, Z. Hammouch, M. A. Noor, R. Ashraf, and Y.-M Chu, Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function, Adv. Differ. Equ. 2020 (2020), no. 1, 1–20, DOI: https://doi.org/10.1186/s13662-020-03108-8.
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Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-46c9b05c-2e0b-4baa-90f9-724cfbb5059e
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