Main Article Content
In this paper we establish Opial type integral inequalities for Widder derivatives and linear di_erential operator. Also, for applications we construct some related inequalities as special cases.
- R. P. Agarwal and P. Y. H. Pang, Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Academic Publishers, Dordrecht, Boston, London 1995.
- R. P. Agarwal and V. Lakshmikantham, Uniqueness and Non uniqueness Criteria for Ordinary Differential Equations, World Scientific, Singapore, 1993.
- G. A. Anastassiou, Advanced inequalities, Vol. 11. World Scientific, 2011.
- M. Andri ´c, A. Barbir, G. Farid and J. Peˇcari ´c, More on certain Opial-type inequality for fractional derivatives and exponentially convex functions, Nonlinear Funct. Anal. Appl., to appear.
- M. Andri ´c, A. Barbir, G. Farid and J. Peˇcari ´c, Opial-type inequality due to Agarwal-Pang and fractional differential inequalities, Integral Transforms Spec. Funct., 25 (4) (2014), 324-335.
- M. Andri ´c, J. Peˇcari ´c and I. Peri ´c, Improvements of composition rule for the Canavati fractional derivatives and applications to Opial-type inequalities, Dynam. Systems. Appl., 20 (2011), 383-394.
- M. Andri ´c, J. Peˇcari ´c and I. Peri ´c, A multiple Opial type inequality for the Riemann-Liouville fractional derivatives, J. Math. Inequal., 7 (1) (2013), 139-150.
- M. Andri ´c, J. Peˇcari ´c and I. Peri ´c, Composition identities for the Caputo fractional derivatives and applications to Opial-type inequalities, Math. Inequal. Appl., 16 (3) (2013), 657-670.
- D. Bainov and P. Simeonov, Integral Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1992.
- G. Farid and J. Peˇcari ´c, Opial type integral inequalities for fractional derivatives, Fractional Differ. Calc., 2 (1) (2012), 31-54.
- G. Farid and J. Peˇcari ´c, Opial type integral inequalities for fractional derivatives II, Fractional Differ. Calc., 2 (2) (2012), 139-155.
- D. Kreider, R. Kuller, and F. Perkins, An Introduction to Linear Analysis, Addison-Wesley Publishing Company, Inc., Reading, Mass., USA, 1966.
- J. D. Li, Opial-type integral inequalities involving several higher order derivatives, J. Math. Anal. Appl., 167 (1) (1992), 98-110.
- D. S. Mitrinovi ´c, J. E. Peˇcari ´c and A. M. Fink, Inequalities involving Functions and Their Integrals ang Derivatives, Kluwer Academic Publishers, Dordrecht, 1991.
- Z. Opial, Sur une in ´egalit ´e, Ann. Polon. Math., 8 (1960), 29-32.
- J. E. Peˇcari ´c, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Inc., 1992.
- D. V. Widder, A Generalization of Taylor's Series, Transactions of AMS, 30 (1) (1928), 126-154.
- D. V. Widder, The Laplace transform, Princeton Uni. Press, New Jersey, 1941.
- D. Willett, The existence-uniqueness theorems for an nth order linear ordinary differential equation, Amer. Math. Monthly, 75 (1968), 174-178.