PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 10 | 1194-1211
Tytuł artykułu

Vectorial fractional integral inequalities with convexity

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1194-1211
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-12-19
Twórcy
  • Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA
Bibliografia
  • [1] G.A. Anastassiou, Fractional Differentiation Inequalities, Research Monograph, (Springer, New York, 2009) http://dx.doi.org/10.1007/978-0-387-98128-4[Crossref]
  • [2] G.A. Anastassiou, Chaos, Soliton. Fract. 42, 365 (2009) http://dx.doi.org/10.1016/j.chaos.2008.12.013[Crossref]
  • [3] G.A. Anastassiou, Chaos, Soliton. Fract. 42, 1523 (2009) http://dx.doi.org/10.1016/j.chaos.2009.03.047[Crossref]
  • [4] G.A. Anastassiou, Chaos, Soliton. Fract. 42, 2080 (2009) http://dx.doi.org/10.1016/j.chaos.2009.03.183[Crossref]
  • [5] G.A. Anastassiou, Mathematical and Computer Modelling 54, 3098 (2011) http://dx.doi.org/10.1016/j.mcm.2011.07.040[Crossref]
  • [6] G.A. Anastassiou, Vectorial Hardy type fractional inequalities, submitted, (2012)
  • [7] D. Baleanu, O.G. Mustafa, R.P. Agarwal, Appl. Math. Lett. 23, 1129 (2010) http://dx.doi.org/10.1016/j.aml.2010.04.049[Crossref]
  • [8] D. Baleanu, O.G. Mustafa, R.P. Agarwal, J. Phys. A: Math. Theor. 43, 385209 (2010) http://dx.doi.org/10.1088/1751-8113/43/38/385209[Crossref]
  • [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)
  • [10] J.A. Canavati, Nieuw Archief Voor Wiskunde 5, 53 (1987)
  • [11] Kai Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, Vol 2004, 1st edition, (Springer, New York, Heidelberg, 2010) http://dx.doi.org/10.1007/978-3-642-14574-2[Crossref]
  • [12] A.M.A. El-Sayed, M. Gaber, Electron. J. Theor. Phys. 3, 81 (2006)
  • [13] R. Gorenflo, F. Mainardi, Essentials of Fractional Calculus, 2000, Maphysto Center, http://www.maphysto.dk/oldpages/events/LevyCAC2000/MainardiNotes/fm2k0a.ps
  • [14] G.D. Handley, J.J. Koliha, J. Pecaric, Fract. Calc. Appl. Anal. 4, 37 (2001)
  • [15] H.G. Hardy, Messenger of Mathematics 47, 145 (1918)
  • [16] S. Iqbal, K. Krulic, J. Pecaric, J. Inequal. Appl. 264347 (2010)
  • [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)
  • [18] T. Mamatov, S. Samko, Fract. Calc. Appl. Anal. 13, 245 (2010)
  • [19] W. Rudin, Real and Complex Analysis, International Student Edition, (Mc Graw Hill, London, New York, 1970)
  • [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)
  • [21] D. Stroock, A Concise Introduction to the Theory of Integration, Third Edition, (Birkhäuser, Boston, Basel, Berlin, 1999)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0210-8
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.