Fractional representation formulae under initial conditions and fractional Ostrowski type inequalities

• Autorzy: Anastassiou G. A.

Identyfikatory

DOI

10.1515/dema-2015-0025

• Języki publikacji: EN

Abstrakty

EN

Here we present very general fractional representation formulae for a function in terms of the fractional Riemann–Liouville integrals of different orders of the function and its ordinary derivatives under initial conditions. Based on these, we derive general fractional Ostrowski type inequalities with respect to all basic norms.

Słowa kluczowe

EN

fractional integral; representation formulae; Ostrowski inequality

PL

całkowanie ułamkowe; nierówność Ostrowskiego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 3
• Strony: 357--378
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Anastassiou G. A.

• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

Bibliografia

• [1] G. Anastassiou, M. Hooshmandasl, A. Ghasemi, F. Moftakharzadeh, Montgomery identities for fractional integrals and related fractional inequalities, JIPAM 10(4) (2009), Article 97, 6 pages.
• [2] D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Inequalities for Functions and their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, Netherlands, 1994.
• [3] S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, USA, 1993.