RIEMANN-LIOUVILLE FRACTIONAL OPIAL INEQUALITIES FOR SEVERAL FUNCTIONS WITH APPLICATIONS

George A. Anastassiou

Title	RIEMANN-LIOUVILLE FRACTIONAL OPIAL INEQUALITIES FOR SEVERAL FUNCTIONS WITH APPLICATIONS
Publication Type	Journal Article
Year of Publication	2008
Authors	Anastassiou, GA
Volume	12
Issue	4
Start Page	377
Pagination	22
Date Published	2008
ISSN	1083-2564
AMS	26A33, 26D10, 26D15, 34A12, 34A99
Abstract	A large variety of very general ${ L_p(1 ≤ p ≤ ∞) }$ form Opial type inequalities ([15]) is presented involving Riemann-Liouville fractional derivatives ([5], [12], [13], [14]) of several functions in different orders and powers. From the established results derive several other particular results of special interest. Applications of some of these special inequalities are given in proving uniqueness of solution and in giving upper bounds to solutions of initial value fractional problems involving a very general system of several fractional differential equations. Upper bounds to various Riemann-Liouville fractional derivatives of the solutions that are involved in the above systems are given too.
URL	http://www.acadsol.eu/en/articles/12/4/2.pdf
Refereed Designation	Refereed
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