Certain fractional integral inequalities using generalized Katugampola fractional integral operator

Asha B. Nale; Satish K. Panchal; Vaijanath L. Chinchane

doi:10.26637/MJM0803/0013

Abstract

The purpose of this paper is to obtain some new fractional integral inequalities involving convex functions by applying generalized Katugampola fractional integral operator.

Keywords:

Generalized Katugampola fractional integral, convex functions and inequality

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Asha B. Nale Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004, India. https://orcid.org/0000-0003-2793-5992
Satish K. Panchal Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004, India.
Vaijanath L. Chinchane Department of Mathematics, Deogiri Institute of Engineering and Management, Aurangabad-431004, India. https://orcid.org/0000-0003-4246-8405

Pages: 809-814
Date Published: 01-07-2020
Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

T.A Aljaaidi and D. B. Pachpatte, Osome Grüss-type inequalities using generalized Katugampola fractional integral, AIMS Mathematics, 5(2)(2020), 1011-1024.

S. Belarbi and Z. Dahmani, On some new fractional integral inequality, J. Inequal. Pure and Appl. Math. Art., $86(10(3))(2009), 1-5$.

D. Baleanu, S. D. Purohit and J. C. Prajapati, Integral inequalities involving generalized Erdélyi-Kober fractional integral operators, Open. Math, 14(2016), 89-99.

V. L. Chinchane, New approach to Minkowski fractional inequalities using generalized K-fractional integral operator, Journal of the Indian. Math. Soc., 1-2(85)(2018), $32-41$.

V. L. Chinchane and D. B. Pachpatte, On some Grüsstype fractional inequalities using Saigo fractional integral operator, Journal of Mathematics, Article ID 527910, Vol.2014 (2014), 1-9.

V. L. Chinchane and D. B. Pachpatte, Note on fractional integral inequality involving convex function using Saigo fractional integral, Indian Journal of Mathematics, 1(61)(2019), 27-39.

V. L. Chinchane and D. B. Pachpatte, On new fractional integral inequalities involving convex functions using Hadamard fractional integral, Indian Journal of Mathematics, 2(31)(2016), 183-192.

Z. Dahmani, A note on some new fractional results involving convex functions, Acta Math. Univ. Comenianae, 81(2)(2012), 241-246.

Z. Dahmani and N. Bedjaoui, Some generalized integral inequalities, J. Advan. Res. Appl. Math., 3(4)(2011), 5866.

Z. Dahmani and H. Metakkel El Ard, Generalization of some integral inequalities using Riemann-Liouville operator, Int. J. Open Problem Compt. Math. 4(4)(2011), $40-46$.

A. A. George, Fractional Differentiation Inequalities, Springer Publishing Company, New York, 2009.

U. N. Katugampola, A new approch to generalized fractional derivatives, Bull. Math. Anal. Appl., 6(4)(2014), $1-15$.

U. N. Katugampola, new fractional integral unifying six existing fractional integral, arXiv: 1612.08596 [math.CA] (2016), 1-6.

S. Kilinc and H. Yildirim, Generalized fractional integral inequalities involving Hypergeometic operators, Int. J. Pure Appl. Math., 101(1)(2015), 71-82.

V. Kiryakova, On two Saigo's fractional integral operator in the class of univalent functions, Fract. Calc. Appl. Anal. 9(2)(2006), 1-10.

A. R. Prabhakaran and K. Srinivasa Rao, Saigo operator of fractional integration of Hypergeometric functions, Int. J. Pure Appl. Math. 81(5)(2012), 755-763.

S. D. Purohit and R. K. Raina, Chebyshev type inequalities for the Saigo fractional integral and their q- analogues, J. Math. Inequal., 7(2)(2013), 239-249.

S. D. Purohit and R. K. Raina, Certain fractional integral inequalities involving the Gauss hypergeometric function, Rev. Tec. Ing. Univ. Zulia 37(2), (2014), 167-175.

M. Saigo, A remark on integral operators involving the Grüss hypergeometric functions, Math. Rep. Kyushu Univ, 11(1978), 135-143.

J. Vanterler da C. Sousa D. S. Oliveira E. Capelas de Oliveira, Grüss- type inequalities by means of generalized fractional integrals, Bull Braz, Math. Soc. New, 50,(2019), 1029-1047.

S.G. Somko, A.A. Kilbas and O.I. Marichev, Fractional Integral and Derivative Theory and Application, Gordon and Breach, Yverdon, Switzerland, 1993.