On some integral inequalities using Hadamard fractional integral

Downloads

DOI:

https://doi.org/10.26637/mjm0101/008

Abstract

In this paper, using Hadamard fractional integral, we establish two main new result on fractional integral inequalities by considering the extended Chebyshev functional in case of synchronous function. The first result concerns with some inequalities using one fractional parameter and other with two parameter.

Keywords:

Chebyshev functional, Hadamard fractional integral, Hadamard fractional derivative and fractional integral inequality

Mathematics Subject Classification:

26D10, 26A33
  • Pages: 62-66
  • Date Published: 01-09-2012
  • Vol. 1 No. 1 (2012): Inaugural Issue :: Malaya Journal of Matematik (MJM)

A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier, Amersterdam, 2006.

D. Baleanu, J.A.T. Machado and C.J. Luo, Fractional Dynamic and Control, Springer, 2012, pp.159-171. DOI: https://doi.org/10.1007/978-1-4614-0457-6

G. A. Anastassiou, Fractional Differentiation Inequalities, Springer Publishing Company, Incorporated, New York, NY, 2009. DOI: https://doi.org/10.1007/978-0-387-98128-4

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

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

Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci., 9(4)(2010), 493-497.

Z. Dahmani, On Minkowski and Hermit-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(1)(2010), 51-58. DOI: https://doi.org/10.15352/afa/1399900993

Z. Dahmani, The Riemann-Liouville operator to genarate some new inequalities, Int. J. Nonlinear Sci., 12(4)(2011), 452-455.

Z. Dahmani, Some results associate with fractional integrals involving the extended Chebyshev, Acta Univ. Apulensis Math. Inform., 27(2011), 217-224.

W. Yang, Some new fractional quantum integral inequalities, Appl. Math. Latt., 25(6)(2012), 963-969. DOI: https://doi.org/10.1016/j.aml.2011.11.005

  • NA

Metrics

Metrics Loading ...

Published

01-09-2012

How to Cite

Vaijanath L. Chinchane, and Deepak B. Pachpatte. “On Some Integral Inequalities Using Hadamard Fractional Integral”. Malaya Journal of Matematik, vol. 1, no. 1, Sept. 2012, pp. 62-66, doi:10.26637/mjm0101/008.