Skip to main content
SpringerLink
Log in

Vectorial fractional integral inequalities with convexity

  • Research Article
  • Published:
Central European Journal of Physics

Abstract

Here we present vectorial general integral inequalities involving products of multivariate convex and increasing functions applied to vectors of functions. As specific applications we derive a wide range of vectorial fractional inequalities of Hardy type. These involve the left and right: Erdélyi-Kober fractional integrals, mixed Riemann-Liouville fractional multiple integrals. Next we produce multivariate Poincaré type vectorial fractional inequalities involving left fractional radial derivatives of Canavati type, Riemann-Liouville and Caputo types. The exposed inequalities are of L p type, p ≥ 1, and exponential type.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G.A. Anastassiou, Fractional Differentiation Inequalities, Research Monograph, (Springer, New York, 2009)

    Book  Google Scholar 

  2. G.A. Anastassiou, Chaos, Soliton. Fract. 42, 365 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. G.A. Anastassiou, Chaos, Soliton. Fract. 42, 1523 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. G.A. Anastassiou, Chaos, Soliton. Fract. 42, 2080 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. G.A. Anastassiou, Mathematical and Computer Modelling 54, 3098 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. G.A. Anastassiou, Vectorial Hardy type fractional inequalities, submitted, (2012)

    Google Scholar 

  7. D. Baleanu, O.G. Mustafa, R.P. Agarwal, Appl. Math. Lett. 23, 1129 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. D. Baleanu, O.G. Mustafa, R.P. Agarwal, J. Phys. A: Math. Theor. 43, 385209 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  9. D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods, in: Series on Complexity, Nonlinearity and Chaos, (World Scientific, Singapore, 2012)

    Google Scholar 

  10. J.A. Canavati, Nieuw Archief Voor Wiskunde 5, 53 (1987)

    MATH  MathSciNet  Google Scholar 

  11. Kai Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, Vol 2004, 1st edition, (Springer, New York, Heidelberg, 2010)

    Book  MATH  Google Scholar 

  12. A.M.A. El-Sayed, M. Gaber, Electron. J. Theor. Phys. 3, 81 (2006)

    Google Scholar 

  13. R. Gorenflo, F. Mainardi, Essentials of Fractional Calculus, 2000, Maphysto Center, http://www.maphysto.dk/oldpages/events/LevyCAC2000/MainardiNotes/fm2k0a.ps

    Google Scholar 

  14. G.D. Handley, J.J. Koliha, J. Pecaric, Fract. Calc. Appl. Anal. 4, 37 (2001)

    MATH  MathSciNet  Google Scholar 

  15. H.G. Hardy, Messenger of Mathematics 47, 145 (1918)

    Google Scholar 

  16. S. Iqbal, K. Krulic, J. Pecaric, J. Inequal. Appl. 264347 (2010)

    Google Scholar 

  17. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, (Elsevier, New York, NY, USA, 2006)

    Google Scholar 

  18. T. Mamatov, S. Samko, Fract. Calc. Appl. Anal. 13, 245 (2010)

    MATH  MathSciNet  Google Scholar 

  19. W. Rudin, Real and Complex Analysis, International Student Edition, (Mc Graw Hill, London, New York, 1970)

    Google Scholar 

  20. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integral and Derivatives: Theory and Applications, (Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993)

    Google Scholar 

  21. D. Stroock, A Concise Introduction to the Theory of Integration, Third Edition, (Birkhäuser, Boston, Basel, Berlin, 1999)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    George A. Anastassiou

Authors
  1. George A. Anastassiou
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Anastassiou, G.A. Vectorial fractional integral inequalities with convexity. centr.eur.j.phys. 11, 1194–1211 (2013). https://doi.org/10.2478/s11534-013-0210-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11534-013-0210-8

Keywords

Search

Navigation