CUBO A Mathematical Journal Vol.13, N° 01, (61–71). March 2011

CONTENTS

q- Fractional Inequalities

George A. Anastassiou

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A., email: ganastss@gmail.com

ABSTRACT

Here we give q-fractional Poincaré type, Sobolev type and Hilbert-Pachpatte type integral inequalities, involving q-fractional derivatives of functions. We give also their generalized versions.

Keywords: q-fractional derivative, q-fractional integral, q-fractional Poincaré inequality, q- fractional Sobolev inequality, q-fractio- nal Hilbert-Pachpatte inequality.

RESUMEN

Estudiamos el tipo q-fraccional Poincaré, el tipo Sobolev y el tipo integral de inecuaciones de Hilbert-Pachpatte, involucrando a q-fraccional derivados de funciones. Damos también las versiones generalizadas.

AMS Subject Classification: 26A24, 26A33, 26A39, 26D10, 26D15, 33D05, 33D60, 81P99.

References

[1] George Anastassiou, Fractional Differentiation Inequalities, Springer, N. York, Heidelberg, 2009.        [ Links ]

[2] H. Gauchman, Integral inequalities in q-Calculus, Computers and Mathematics with Applications, 47 (2004), 281-300.        [ Links ]

[3] P. Rajkovic, S. Marinkovic, M. Stankovic, Fractional integrals and derivatives in q-Calculus, Applicable Analysis and Discrete Mathematics, 1 (2007), 311-323.        [ Links ]

[4] M. Stankovic, P. Rajkovic, S. Marinkovic, On q-fractional derivatives of Riemann Liouville and Caputo type, arXiv: 0909.0387 v1[math.CA] 2 Sept. 2009        [ Links ]

Received: October 2009.

Revised: November 2009.