Desigualdades integrales fraccionales y sus q-análogos
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Desigualdades integrales, operadores integrales fraccionales, operadores q-integrales fraccionales.Resumen
El objeto de este trabajo es establecer algunas desigualdades que envuelven operadores integrales de Saigo. Se usa el calculo q-fraccional para obtener varios resultados en la teoría de las desigualdades q-integrales. Los resultados dados anteriormente por Purohit y Raina (2013) y Sulaiman (2011) son casos especiales de los obtenidos en este trabajo.
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Referencias
G.A. Anastassiou, Advances on Fractional Inequalities, Springer Briefs in Mathematics, Springer, New York, 2011.
Z. Denton, A.S. Vatsala, Monotonic iterative technique for finit system of nonlinear Riemann-Liouville fractional differential equations, Opuscula Mathematica, 31(3)(2011), 327-339.
S.L. Kalla and Alka Rao, On Gr u˙ ss type inequality for hypergeometric fractional integrals, Le Ma- tematiche, 66 (1)(2011), 57-64.
V. Lakshmikantham and A.S. Vatsala, Theory of fractional differential inequalities and applications, Commu. Appl. Anal., 11 (2007), 395-402.
J.D. Ramírez, A.S. Vatsala, Monotonic iterative technique for fractional differential equations with periodic boundary conditions, Opuscula Mathematica, 29(3)(2009), 289-304.
S.D. Purohit and R.K. Raina, Chebyshev type inequalities for the Saigo fractional integrals and their q -analogues, J. Math. Inequal., 7(2) (2013), 239-249.
P.L. Chebyshev, Sur les expressions approximatives des integrales definies par les autres prises entre les mêmes limites, Proc. Math. Soc. Charkov, 2(1882), 93-98.
W.T. Sulaiman, Some new fractional integral inequalities, J. Math. Anal., 2(2) (2011), 23-28.
M. Saigo, A remark on integral operators involving the Gauss hypergeometric functions, Math. Rep. Kyushu Univ., 11 (1978) 135-143.
V.S. Kiryakova, Generalized Fractional Calculus and Applications (Pitman Res. Notes Math. Ser. 301), Longman Scientific & Technical, Harlow, 1994.
R.K. Raina, Solution of Abel-type integral equation involving the Appell hypergeometric function, Integral Transforms Spec. Funct., 21(7)(2010), 515-522.
G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
M.H. Annaby and Z.S. Mansour, q -Fractional Calculus and Equations (Lecture Notes in Mathematics 2056), Springer-Verlag Berlin Heidelberg, 2012.
H. Öğünmez, and U.M. Özkan, Fractional quantum integral inequalities, J. Inequal. Appl., Volume 2011, Article ID 787939, 7 pp.
R.P. Agarwal, Certain fractional q -integrals and q -derivatives, Proc. Camb. Phil. Soc., 66 (1969), 365-370.
W.A. Al-Salam, Some fractional q -integrals and q -derivatives, Proc. Edin. Math. Soc., 15(1966), 135-140.
M. Garg and Lata Chanchlani, q -Analogue of Saigo’s fractional calculus operators, Bull. Math. Anal. Appl., 3(4) (2011), 169-179.
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