Finally, we wrap-up this lecture with our new result which achieves a competitive factor of Õ(log k log n) for the k-server problem on n nodes1. This is joint work with Nikhil Bansal, Niv Buchbinder, and Aleksander Madry. Our basic approach is based on the framework of [CMP08]. The key idea in our work is that instead of using the allocation problem (as suggested by [CMP08]), we use the fractio...

fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order.the purpose of this work is to use hadamard fractional integral to establish some new integral inequalities of gruss type by using one or two parameters which ensues four main results . furthermore, other integral inequalities of reverse m...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

‎in this paper, we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (pmsm) system. the necessary condition for the existence of chaos in the fractional-order pmsm system is deduced and an active controller is developed based on the stability theory for fractional systems. the presented control scheme  is simple and flexible, and it is suitable both fo...

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

In this paper, a new numerical method for solving the fractional Riccati differential  equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon  fractional-order Bernoulli functions approximations. First, the  fractional-order Bernoulli functions and  their properties are  presented. Then, an operational matrix of fractional order integration...

In the human circulation, factor VII is present in relatively low plasma concentration (0.01 microM) and has been reported to have a short half-life (t(1/2); 6 h). In contrast, prothrombin is present in a relatively high plasma concentration (2 microM) and has a relatively long catabolic half-life (t(1/2) = approximately 2-3 days). This report examines the metabolic characteristics of purified ...

effects of formulation parameters on the fractional release profile of diclofenac sodium from matrices having the manufacturing formulation ingredients are studied. as a content of cetyl alcohol (rate controlling agent) in the matrix increases, the fractional release decreases. the fractional release increases either by increasing sucrose content outside the granule or by decreasing sucrose con...

In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...