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Progress in Fractional Differentiation and Applications
An International Journal



Certain New Integral Inequalities Involving Erdelyi-Kober ` Operators

Naresh Menaria, Faruk Uc¸ar, Sunil Dutt Purohit,
Abstract :
In this article, the Erdelyi-Kober fractional integral operator is employed to generate certain new classes of integral ` inequalities using a family of n positive functions, (n ∈ N). Certain special cases and consequent results of the main results are also pointed out.


Existence of solutions of multi-point boundary value problems for fractional differential systems with impulse effects

Yuji Liu,
Abstract :
In this article, we present a new method for converting the considered impulsive systems to integral systems. As application of this method, we establish existence results for solutions of boundary value problems for nonlinear impulsive fractional differential systems. Our analysis relies on the well known Schauders fixed point theorem. The mistakes in [Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89(2011), 1-19] and [Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance, J, Appl, Math, Comput., 39(2012) 421-443] are corrected, see Remark 2.1.


On the existence and uniqueness of solutions for nonlinear fractional differential equations with fractional boundary conditions

Brahim Tellab,
Abstract :
This paper concerns some new existence and uniqueness results obtained by applying classical fixed point theorems for a class of Riemann-Liouville fractional differential equations with fractional boundary conditions.


Design and Analysis of Fractional Order Controller for 2-D Gantry Crane System

Abhaya Pal Singh,
Abstract :
This paper demonstrate that fractional order calculus could provide better description and model various real dynamic systems more adequately than the integer order ones. The proposed under-actuated dynamical system is 2-D Gantry crane that has two degrees of freedom and one control input. Precise control of a crane is essential as its failure may cause accidents and may harm the people around it. In this paper we design an integer order PID (IOPID) controller and a fractional order PID (FOPID) controller for the 2-D Gantry crane system and then compared their performances. The purpose of the controllers is to control the position of the trolley and the swing angle of the cable through which the load is suspended.



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