223 research outputs found
Measurement of the Communication Possibility of Service Requests for Multiservers in Parallel Connection in Cloud Computing Systems
Newly, growing amount of dataādemanding applications arrangement with continuous fluctuating data substances, have been investigated by many researchers recently. In these applications, the underlying data management system must support new types of the spaceātime changing that indicates to the paths of the cloud computing system (CCS). The timeāspace changing causes change in the dimension of data and, consequently, in the CCS. One of the solutions regarding this case is suggesting an integrated cloud computing system (ICCS). In this effort, we introduce a new ICCS, based on fractional formal operators, taking into account the symmetrical delay in it. This model is useful for higher dimensional data, moving data, and chaos data. Moreover, we employ a fractional differential method to discover the paths (outcomes) of the system by minimizing the cost function. The proposed system delivers a sequence of paths that converge to the optimal path. The theoretical technique is supported by the applications
Ulam stability for fractional differential equations in the sense of Caputo operator
In this paper, we consider the Hyers-Ulam stability for the following fractional differential equations, in the sense ofcomplex Caputo fractional derivative defined, in the unit disk: cDĆzf(z)=G(f(z), cDĆ”zf(z),zfā(z);z) 0<Ć”<1<Ć<2 . Furthermore,a generalization of the admissible functions in complex Banach spaces is imposed and applications are illustrated
On the existence and uniqueness of solutions of a class of fractional differential equations
AbstractIn this paper, we investigate the existence and uniqueness of solutions for the following class of multi-order fractional differential equationsDĪ²1Ī³1,Ī“1āÆDĪ²nĪ³n,Ī“nu(t):=āi=1nDĪ²iĪ³i,Ī“iu(t):=DĪ²i,nĪ³i,Ī“iu(t)=f(t,u(t)),tā[0,1],u(0)=0,āi=1nĪ“iā©½1,Ī³i>0,Ī²i>0,1ā©½iā©½n, where DĪ²i,nĪ³i,Ī“i denotes the generalized ErdĆ©lyiāKober operator of fractional derivative of order Ī“i. Moreover, some properties concerning the positive, maximal, minimal, and continuation of solutions are obtained
Integral Operator Defined by k-th Hadamard Product
We introduce an integral operator on the class A of analytic functions in the unit disk involving k Ćā{ th Hadamard product (convolution) corresponding to the differential operator defined recently by Al-Shaqsi and Darus. New classes containing this operator are studied. Characterization and other properties of these classes are studied. Moreover, subordination and superordination results involving this operator are obtained
Geometric properties of the complex Baskakov-Stancu operators in the unit disk
In this article, we determine certain conditions under which the partial sums involving thecomplex Baskakov-Stancu operators of analytic univalent functions of bounded turning are also of boundedturning. Moreover, we consider some geometric properties such as starlikeness and convexity for these partialsums. The lower bound of the partial sums of univalent functions is computed using the lower bound of thecomplex Baskakov-Stancu operators of analytic function
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