Here first we collect and develop necessary background on time scales required for this article. Then we present time scales integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert–Pachpatte. We give also the generalized analogs of all these inequalities involving high order delta derivatives of functions on time scales. We finish with lots of applications: all these ine...

This paper addresses the bifurcation control of a fractional-order Lokta-Volterra predator-prey model by using delay feedback control. By employing time as parameter, conditions are gained for controlled systems. Then, it indications that onset can be postponed gain decreases. An example numerical results ultimately exploited to validate correctness proposed scheme.

a f (x) dx− b− a n n ∑ i=1 f (a+ xi (b− a)) ∣∣∣∣ 5 2m+ 5 4 (b− a)m+1 (m+ 1)! (S − s) (?) holds, where S := supa5x5b f (m)(x), s := infa5x5b f (m)(x) and for suitable x1, x2, . . . , xn. It is worth noticing that n,m are arbitrary numbers. This means that the estimate in (?) is more accurate whenm is large enough. Our approach is also elementary. © 2010 Elsevier Ltd. All rights reserved.

Generalizations of some Steffensen's inequalities for the class higher order convex functions are obtained in present study. To prove results, preliminary lemmas established by using extended Montgomery identities via Taylor's formula on time scales. Furthermore, Ostrowski type also established, along with optimization constant. Moreover, newly results discussed discrete and quantum calculus as...