A grüss type integral inequality associated with gauss hypergeometric function fractional integral operator
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In this paper, we aim at establishing a generalized fractional integral version of Gr\"uss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known results.
Abstract
In this paper, we aim at establishing a generalized fractional integral version of Gr\"uss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known results.
참고문헌 (51)
- G. A. Anastassiou, "Fractional Differentiation Inequalities" (2009), Springer Publishing Company
- G. A. Anastassiou, "Advances on Fractional Inequalities, Springer Briefs in Mathematics" (2011), Springer
- G. A. Anastassiou, "Fractional representation formulae and right fractional inequalities", Math. Comput. Modelling, 54(11-12), pp.3098~3115 (2011)
- A. Atangana, "The use of fractional order derivative to predict the groundwater flow", Math. Probl. Eng, pp.9~ (2013)
- A. Atangana, "A novel integral operator transform and its application to some FODE and FPDE with some kind of singularities", Math. Probl. Eng, pp.7~ (2014)
- A. Atangana, "A note on fractional order derivatives and table of fractional derivatives of some special functions", Abstr. Appl. Anal, pp.8~ (2013)
- D. Baleanu, "On fractional integral inequalities involving hypergeometric operators", Chin. J. Math, pp.5~ (2014)
- D. Baleanu, "On Gr¨uss type integral inequality involving the Saigo’s fractional integral operators", J. Comput. Anal. Appl, 19(3), pp.480~489 (2015)
- P. Cerone, "New upper and lower bounds for the Chebyshev functional", J. Inequal. Pure App. Math, 3(2), pp.13~ (2002)
- P. L. Chebyshev, "Chebyshev, Sur les expressions approximatives des integrales definies par les autres prises entre les mˆemes limites", Proc. Math. Soc. Charkov, 2, pp.93~98 (1882)
- J. Choi, "Some new Saigo type fractional integral inequalities and their q-analogues", Abstr. Appl. Anal, pp.11~ (2014)
- 최준상, "Certain Fractional Integral Inequalities Involving Hypergeometric Operators", East Asian Mathematical Journal, 30(3), pp.283~291 (2014), 영남수학회[DOI]
- 최준상, "CERTAIN NEW PATHWAY TYPE FRACTIONAL INTEGRAL INEQUALITIES", 호남수학학술지, 36(2), pp.455~465 (2014), 호남수학회
- J. Choi, "Certain integral transform and fractional integral formulas for the generalized Gauss hypergeometric functions", Abstr. Appl. Anal, 2014(7pages) (2014)
- L. Curiel, "A generalization of the integral operators involving the Gauss’hypergeometric function", Rev. T´ech. Ingr. Unlv. Zulla, 19(1), pp.17~22 (1996)
- Z. Dahmani, "New weighted Gr¨uss type inequalities via (, ) fractional q-integral inequalities", IJIAS, 1(1), pp.76~83 (2012)
- Z. Dahmani, "New generalizations of Gr¨uss inequality using Riemann-Liouville fractional integrals", Bull. Math. Anal. Appl, 2(2), pp.93~99 (2010)
- A. Debbouche, "Nonlocal nonlinear integrodifferential equations of fractional orders", Bound. Value Probl, 78, pp.10~ (2012)
- Z. Denton, "Monotonic iterative technique for finite system of nonlinear Riemann-Liouville fractional differential equations", Opusc. Math, 31(3), pp.327~339 (2011)
- S. S. Dragomir, "A generalization of Gr¨uss’s inequality in inner product spaces and applications", J. Math. Anal. Appl, 237(1), pp.74~82 (1999)
- S. S. Dragomir, "A Gr¨uss type inequality for sequences of vectors in inner product spaces and applications", J. Inequal. Pure Appl. Math, 1(2) (2000)
- S. S. Dragomir, "Some integral inequalities of Gr¨uss type", Indian J. Pure Appl. Math, 31(4), pp.397~415 (2000)
- S. S. Dragomir, "Operator Inequalities of the Jensen, ˇCebyˇsev and Gr¨uss Type, Springer Briefs in Mathematics" (2012), Springer
- S. S. Dragomir, "An inequality of Ostrowski-Gr¨uss’ type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules", Comput. Math. Appl, 13(11), pp.15~20 (1997)
- H. Gauchman, "Integral inequalities in q-calculus", Comput. Math. Appl, 47(2-3), pp.281~300 (2004)
- B. Gavrea, "Improvement of some inequalities of Chebysev-Gr¨uss type", Comput. Math. Appl, 64(5), pp.2003~2010 (2012)
- D. Gr¨uss, "¨Uber das maximum des absoluten Betrages von 1(b−a) R b a f (x) g (x) dx −1(b−a)2 R b a f (x) dx R b a g (x) dx", Math. Z, 39(1), pp.215~226 (1935)
- S. L. Kalla, "On Gr¨uss type inequality for a hypergeometric fractional integrals", Matematiche, 66(1), pp.57~64 (2011)
- G. Kapoor, "On some discrete Gr¨uss type inequalities", Inter. J. Math. Sci. Appl, 2(2), pp.729~734 (2012)
- V. Kiryakova, "Generalized Fractional Calculus and Applications, (Pitman Res. Notes Math. Ser. 301)" (1994), Longman Scientific & Technical
- V. Lakshmikantham, "Theory of fractional differential inequalities and applications", Commun. Appl. Anal, 11(3-4), pp.395~402 (2007)
- Z. Liu, "Some Ostrowski-Gr¨uss type inequalities and applications", Comput. Math. Appl, 53(1), pp.73~79 (2007)
- Y. Liu, "Existence results for a coupled system of nonlinear singular fractional differential equations with impulse effects", Math. Probl. Eng (2013)
- M. Mati´c, "Improvement of some inequalities of Euler-Gr¨uss type", Comput. Math. Appl, 46(8-9), pp.1325~1336 (2003)
- M. A. Mercer, "An improvement of the Gr¨uss inequality", J. Inequal. Pure Appl. Math, 6(4), pp.93~ (2005)
- N. A. Mir, "Some inequalities of Ostrowski and Gr¨uss type for triple integrals on time scales", Tamkang J. Math, 42(4), pp.415~426 (2011)
- D. S. Mitrinovi´c, "Classical and New Inequalities in Analysis" (1993), Kluwer Academic
- S. K. Ntouyas, "Certain Chebyshev type integral inequalities involving Hadamard’s fractional operators", Abstr. Appl. Anal, pp.7~ (2014)
- U. M. ¨Ozkan, "Gr¨uss type inequalities for double integrals on time scales", Comput. Math. Appl, 57(3), pp.436~444 (2009)
- B. G. Pachpatte, "On Gr¨uss type integral inequalities", J. Inequal. Pure Appl. Math, 3(1), pp.5~ (2002)
- B. G. Pachpatte, "A note on Chebyshev-Gr¨uss inequalities for differentiable functions", Tamsui Oxf. J. Math. Sci, 22(1), pp.29~36 (2006)
- S. D. Purohit, "Chebyshev type inequalities for the Saigo fractional integrals and their q-analogues", J. Math. Inequl, 7(2), pp.239~249 (2013)
- S. D. Purohit, "Certain fractional integral inequalities involving the Gauss hypergeometric function", Rev. T´ec. Ing. Univ. Zulia, 37(2), pp.167~175 (2014)
- J. D. Ram´ırez, "Monotonic iterative technique for fractional differential equations with periodic boundary conditions", Opusc. Math, 29(3), pp.289~304 (2009)
- M. Saigo, "A remark on integral operators involving the Gauss hypergeometric functions", Math. Rep. Kyushu Univ, 11(2), pp.135~143 (1978)
- H. -R. Sun, "Existence of solutions for Sturm-Liouville boundary value problem of impulsive differential equations", Abstr. Appl. Anal, 2012, pp.19~ (2012)
- J. Tariboon, "Some new Riemann-Liouville fractional integral inequalities", Int. J. Math. Math. Sci, 2014, pp.6~ (2014)
- G. Wang, "Certain Gr¨uss type inequalities involving the generalized fractional integral operator", J. Inequal. Appl, 2014, pp.8~ (2014)
- W. Yang, "On weighted q-ˇCebyˇsev-Gr¨uss type inequalities", Comput. Math. Appl, 61(5), pp.1342~1347 (2011)
- Z. -H. Zhao, "Asymptotic behavior of solutions to abstract stochastic fractional partial integrodifferential equations", Abstr. Appl. Anal, 2013, pp.8~ (2013)
- C. Zhu, "Some new fractional q-integral Gr¨uss-type inequalities and other inequalities", J. Inequal. Appl, 2012, pp.299~ (2012)
