Desigualdades del tipo Minkowski y Hölder con una nueva integral fraccionariaa generalizada
Palabras clave:
Fractional integral inequalities generalized fractional integral operator Desigualdades fraccionales integrales Operador integral fraccionario generalizado
Resumen
El presente estudio se refiere a algunas desigualdades de tipo Minkovski y Hölder usando un nuevo operador integral fraccional generalizado del tipo de Raina. Usando el modelo de función generalizada de Raina, $ \mathcal{F}_{\rho,\lambda }^{\sigma} $, que involucran ciertos parámetros y una secuencia acotada de números reales positivos, se da una nueva definición de integral fraccional generalizada y de esto se deducen algunos otros operadores integrales fraccionarios clásicos. También la validez de los resultados principales en el marco de Riemman se comprueban las integrales fraccionarias de Liouville, Hadamard, Katugampola, Prabhakar y Salim.
Visitas al artículo
244
Descargas
La descarga de datos todavía no está disponible.
Referencias
[1] B. Acay, E. Bas and T. Abdeljawad, Fractional economic models based on market equilibrium in the
frame of di erent type kernels, Chaos Solitons Fractals 130:109438 (2020), 1–19
[2] R. P. Agarwal, M-J. Luo and R. K. Raina, On Ostrowski type inequalities, Fasciculli Mathematica 56
(2016), 5–27.
[3] A. Alaria, A. M. Khan, D. L. Suthar and D. Kumar, Application of fractional operators in modelling
for charge carrier transport in amorphous semiconductor with multiple trapping, International Journal
of Applied and Computational Mathematics 50(6) (2019), 1–10
[4] A. Atangana, Derivative with a new parameter. Theory,Methods and Applications, Academic Press
Elsevier, London, 2016.
[5] A. Atangana and D. Baleanu, New fractional derivatives with non-local and non-singular kernel:
theory and applications to heat transfer model, Therm. Sci. 20 (2016), 763-?769.
[6] V. Berdnikov, and V. Lokhin, Synthesis of guaranteed stability regions of a nonstationary nonlinear
system with a fuzzy controller, Civil Engineering Journal 50(1) (2019), 107–116
[7] L. Bougo a, On Minkowski and Hardy Integral Inequalities. Jounal of Inequalities in Pure and Applied
Mathematics 7(2) (2006), 1–15.
[8] Z. Chen, G. Farid, A. U. Rehman and N. Latif, Estimations of fractional integral operators for convex
functions and related results, Advances in Di erence equations 2020:163 (2020, 1–18.
[9] H. Chen and U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamard-Fej er type Inequalities
for Generalized Fractional Integrals, J. Math. Anal. Appl. 446 (2017), 1274–1291
[10] 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. Di er. Equ. 2020:647
(2020), 1–20
[11] J. Choi and P. Agarwal, Certain Fractional Integral Inequalities Involving Hypergeometric Operators,
East Asian Math. J. 30(3) (2014), 283–291.
[12] Z. Dahmani, On Minkowski and Hermite-Hadamard Integral Inequalities Via Fractional Integration.
Annals of Functional Analysis 1(1) (2010), 51–58.
[13] S.S. Dragomir, E. Set and M.E. O zdemir, On the Hermite-Hadamard Inequality and Other Integral
Inequalities Involving Two Functions. Journal of Inequalities and Applications 2010:148102 (2010),
1–9.
[14] R. S. Dubey and P. Goswami, Some fractional integral inequalities for the Katugampola integral operator,
AIMS Mathematics 4(2) (2019), 193–198.
[15] A. Fernandez, D. Baleanu and H. M. Srivastava, Series representations for models of fractional calculus
involving generalised Mittag–Le er functions, Commun. Nonlinear Sci. Numer. Simul. 67 (2019),
517-?527.
[16] R. Garra, R. Gorenflo, F. Polito and Z. Tomovski, Hilfer–Prabhakar derivative and some applications,
Appl. Math.Comput. 242 (2014), 576-?589.
[17] R. Garra, R. Garrappa, The Prabhakar or three parameter Mittag-Le er function: Theory and application,
Commun. Nonlinear Sci. Numer. Simul. 56 (2018), 314-?329.
[18] R. Gorenflo, A. A. Kilbas, F. Mainardi and S. V. Rogosin,Mittag-Le er functions, related topics and
applications, Springer, Berlin, 2014.
[19] J. Hadamard, Essai sur l etude des fonctions donnees par leur developpement de Taylor, Journal Math.
Pures et Appl. Ser 4 8 (1892), 101–186.
[20] J. E. Hern andez Hern andez and M. Vivas-Cortez, Hermite–Hadamard Inequalities type for Raina’s
Fractional Integral Operator using convex functions, Rev. Mat. Teor. Apl. 26(1) (2019), 1–19.
[21] T. U. Khan, M.A. Khan, Generalized conformable fractional integral operators, J. Comput. Appl.
Math. 346 (2019), 378?389.
[22] M. A. Khan and T. U. Khan, Generalized Conformable Fractional Operators and Their Applications,In
: Fractional Order Analysis: Theory, Methods and Applications (Chapter 2) , JohnWiley & Sons, Ltd.,
43–89, 2020.
[23] U. N. Katugampola, A New Approach to Generalized Fractional Derivatives, Bull. Math. Anal. Appl.,
6 (2014), 1–15.
[24] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Di erential
Equations, North-Holland Mathematics Studies Vol 204., Elsevier, Amsterdam, The Netherlands,
2006.
[25] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Di erential Equations,
Wiley, New York, 1993.
[26] P. O. Mohammed and T. Abdeljawad, Integral inequalities for a fractional operator of a function with
respect to another function with nonsingular kernel, Advances in Di erence Equations 2020 (363)
(2020), 1–19
[27] K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, San Diego, 1974.
[28] T. R. Prabhakar, A Singular Integral Equation With a Generalized Mittag-Le er function in the kernel,
Yokohama Math. J. 19 (1971), 7–15
[29] F. Polito and ˘ Z. Tomovski, Some properties of Prabhakar-type fractional calculus operators, Fractional
Di erential Calculus 6(1) (2016), 73–94.
[30] X. Qiang, G. Farid and J. Pe˘cari c, Generalized fractional integral inequalities for exponentially
(s;m) convex functions , Journal of inequalities and applications 2020:70 (2020), 1–18.
[31] R. K. Raina, On Generalized Wright’s Hypergeometric functions and Fractional Calculus Operator,
East Asian Mathematical Journal 21(2) (2005), 191–203.
[32] T.O. Salim and A. W. Faraj, A generalization of Mittag-Le er function and integral operator associated
with fractional calculus, J. Fract. Calc. Appl. 3(2012), 1–13.
[33] T. Sandev, Generalized Langevin Equation and the Prabhakar Derivative, Mathematics 5 (2017), 66-76.
[34] S. G.Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications,
Taylor & Francis, London, 2002.
[35] J. V.Sousa and E. C. Oliveira, The Minkowski?s inequality by means of a generalized fractional integral,
AIMS Mathematics 3(1) (2018), 131?-147
[36] T. Tunu uc , H. Budak, F. Usta and M.Z. Sarikaya, On new generalized fractional integral operators
and related inequalities, Konuralp Journal of Mathematics 8(2) (2020), 268–278.
[37] M. Vivas-Cortez, A. Kashuri and J. E. Hern andez Hern andez, Trapezium-Type Inequalities for Raina’s
Fractional Integrals Operator Using Generalized Convex Functions, Symmetry 12 (2020), 1–17.
91
frame of di erent type kernels, Chaos Solitons Fractals 130:109438 (2020), 1–19
[2] R. P. Agarwal, M-J. Luo and R. K. Raina, On Ostrowski type inequalities, Fasciculli Mathematica 56
(2016), 5–27.
[3] A. Alaria, A. M. Khan, D. L. Suthar and D. Kumar, Application of fractional operators in modelling
for charge carrier transport in amorphous semiconductor with multiple trapping, International Journal
of Applied and Computational Mathematics 50(6) (2019), 1–10
[4] A. Atangana, Derivative with a new parameter. Theory,Methods and Applications, Academic Press
Elsevier, London, 2016.
[5] A. Atangana and D. Baleanu, New fractional derivatives with non-local and non-singular kernel:
theory and applications to heat transfer model, Therm. Sci. 20 (2016), 763-?769.
[6] V. Berdnikov, and V. Lokhin, Synthesis of guaranteed stability regions of a nonstationary nonlinear
system with a fuzzy controller, Civil Engineering Journal 50(1) (2019), 107–116
[7] L. Bougo a, On Minkowski and Hardy Integral Inequalities. Jounal of Inequalities in Pure and Applied
Mathematics 7(2) (2006), 1–15.
[8] Z. Chen, G. Farid, A. U. Rehman and N. Latif, Estimations of fractional integral operators for convex
functions and related results, Advances in Di erence equations 2020:163 (2020, 1–18.
[9] H. Chen and U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamard-Fej er type Inequalities
for Generalized Fractional Integrals, J. Math. Anal. Appl. 446 (2017), 1274–1291
[10] 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. Di er. Equ. 2020:647
(2020), 1–20
[11] J. Choi and P. Agarwal, Certain Fractional Integral Inequalities Involving Hypergeometric Operators,
East Asian Math. J. 30(3) (2014), 283–291.
[12] Z. Dahmani, On Minkowski and Hermite-Hadamard Integral Inequalities Via Fractional Integration.
Annals of Functional Analysis 1(1) (2010), 51–58.
[13] S.S. Dragomir, E. Set and M.E. O zdemir, On the Hermite-Hadamard Inequality and Other Integral
Inequalities Involving Two Functions. Journal of Inequalities and Applications 2010:148102 (2010),
1–9.
[14] R. S. Dubey and P. Goswami, Some fractional integral inequalities for the Katugampola integral operator,
AIMS Mathematics 4(2) (2019), 193–198.
[15] A. Fernandez, D. Baleanu and H. M. Srivastava, Series representations for models of fractional calculus
involving generalised Mittag–Le er functions, Commun. Nonlinear Sci. Numer. Simul. 67 (2019),
517-?527.
[16] R. Garra, R. Gorenflo, F. Polito and Z. Tomovski, Hilfer–Prabhakar derivative and some applications,
Appl. Math.Comput. 242 (2014), 576-?589.
[17] R. Garra, R. Garrappa, The Prabhakar or three parameter Mittag-Le er function: Theory and application,
Commun. Nonlinear Sci. Numer. Simul. 56 (2018), 314-?329.
[18] R. Gorenflo, A. A. Kilbas, F. Mainardi and S. V. Rogosin,Mittag-Le er functions, related topics and
applications, Springer, Berlin, 2014.
[19] J. Hadamard, Essai sur l etude des fonctions donnees par leur developpement de Taylor, Journal Math.
Pures et Appl. Ser 4 8 (1892), 101–186.
[20] J. E. Hern andez Hern andez and M. Vivas-Cortez, Hermite–Hadamard Inequalities type for Raina’s
Fractional Integral Operator using convex functions, Rev. Mat. Teor. Apl. 26(1) (2019), 1–19.
[21] T. U. Khan, M.A. Khan, Generalized conformable fractional integral operators, J. Comput. Appl.
Math. 346 (2019), 378?389.
[22] M. A. Khan and T. U. Khan, Generalized Conformable Fractional Operators and Their Applications,In
: Fractional Order Analysis: Theory, Methods and Applications (Chapter 2) , JohnWiley & Sons, Ltd.,
43–89, 2020.
[23] U. N. Katugampola, A New Approach to Generalized Fractional Derivatives, Bull. Math. Anal. Appl.,
6 (2014), 1–15.
[24] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Di erential
Equations, North-Holland Mathematics Studies Vol 204., Elsevier, Amsterdam, The Netherlands,
2006.
[25] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Di erential Equations,
Wiley, New York, 1993.
[26] P. O. Mohammed and T. Abdeljawad, Integral inequalities for a fractional operator of a function with
respect to another function with nonsingular kernel, Advances in Di erence Equations 2020 (363)
(2020), 1–19
[27] K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, San Diego, 1974.
[28] T. R. Prabhakar, A Singular Integral Equation With a Generalized Mittag-Le er function in the kernel,
Yokohama Math. J. 19 (1971), 7–15
[29] F. Polito and ˘ Z. Tomovski, Some properties of Prabhakar-type fractional calculus operators, Fractional
Di erential Calculus 6(1) (2016), 73–94.
[30] X. Qiang, G. Farid and J. Pe˘cari c, Generalized fractional integral inequalities for exponentially
(s;m) convex functions , Journal of inequalities and applications 2020:70 (2020), 1–18.
[31] R. K. Raina, On Generalized Wright’s Hypergeometric functions and Fractional Calculus Operator,
East Asian Mathematical Journal 21(2) (2005), 191–203.
[32] T.O. Salim and A. W. Faraj, A generalization of Mittag-Le er function and integral operator associated
with fractional calculus, J. Fract. Calc. Appl. 3(2012), 1–13.
[33] T. Sandev, Generalized Langevin Equation and the Prabhakar Derivative, Mathematics 5 (2017), 66-76.
[34] S. G.Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications,
Taylor & Francis, London, 2002.
[35] J. V.Sousa and E. C. Oliveira, The Minkowski?s inequality by means of a generalized fractional integral,
AIMS Mathematics 3(1) (2018), 131?-147
[36] T. Tunu uc , H. Budak, F. Usta and M.Z. Sarikaya, On new generalized fractional integral operators
and related inequalities, Konuralp Journal of Mathematics 8(2) (2020), 268–278.
[37] M. Vivas-Cortez, A. Kashuri and J. E. Hern andez Hern andez, Trapezium-Type Inequalities for Raina’s
Fractional Integrals Operator Using Generalized Convex Functions, Symmetry 12 (2020), 1–17.
91
Publicado
2021-08-17
Cómo citar
Vivas-Cortez, M., & Hernández Hernández, J. E. (2021). Desigualdades del tipo Minkowski y Hölder con una nueva integral fraccionariaa generalizada. Revista MATUA ISSN: 2389-7422, 8(1), 74-91. Recuperado a partir de https://investigaciones.uniatlantico.edu.co/revistas/index.php/MATUA/article/view/3008
Sección
Artículos
