n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

The accuracy of the National Research Council 2.1 m cesium beam frequency standard has been re-evaluated using the two NRC hydrogen masers as stable comparison standards. At the time of re-evaluation, the various uncertainties gave rise to an error limit of :!:3.8 x 10-12, with a most probable value of :!:1.5 x 10-12 if they were assumed to be random. Mter application of all corrections, the ag...

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.

‎In this paper‎, ‎we develop the theory of hybrid differential‎ ‎equations on time scales‎. ‎An existence theorem for hybrid‎ ‎differential equations on time scales is given under Lipschitz ‎conditions‎. ‎Some fundamental fractional differential inequalities‎ ‎are also established which are utilized to prove the existence of‎ ‎extremal solutions‎. ‎Necessary tools are considered and the‎ ‎compa...