Abstract
A large variety of Lp(p 0) form very general Opial type inequalities arepresented engaging different order generalized fractional derivatives of a function. These arebased on a generalization of Taylor’s formula for generalized fractional derivatives. In the finalresults of this work, a monotonicity property of the involved function/highest-order generalizedfractional derivative is used.
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References
Agarwal, R. P.: Sharp Opial-type inequalities involving r-derivatives and their applications,Tôhoku Math. J. 47 (1995), 567–593.
Agarwal, R. P. and Pang, P. Y. H.: Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Acad. Publ., Dordrecht, 1995.
Bainov, D. and Simeonov, P.: Integral Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, 1992.
Canavati, J. A.: The Riemann–Liouville integral,Nieuw Arch. Wisk. 5(1) (1987), 53–75.
Fink, A. M.: On Opial’s inequality for f (n),Proc. Amer. Math. Soc. 115(1) (1992), 177–181.
Gradshteyn, I. S. and Ryzhik, I. M.: Table of Integrals, Series, and Products, Academic Press, New York, 1980.
Opial, Z.: Sur une inégalité,Ann. Polon. Math. 8 (1960), 29–32.
Pang, P. Y. H. and Agarwal, R. P.: On an Opial type inequality due to Fink,J. Math. Anal. Appl. 196 (1995), 748–753.
Whittaker, E. T. and Watson, G. N.: A Course in Modern Analysis, Cambridge Univ. Press, Cambridge, 1927.
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Anastassiou, G.A. General Fractional Opial Type Inequalities. Acta Applicandae Mathematicae 54, 303–317 (1998). https://doi.org/10.1023/A:1006154105441
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DOI: https://doi.org/10.1023/A:1006154105441