Wyniki wyszukiwania - Biblioteka Nauki

1

On subordination for classes of non-Bazilevic type

100%

Ibrahim R. W. , Darus M. , Tuneski N.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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2010

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tom 64

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nr 2

EN

We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevic type in the open unit disk. By using Jack’s lemma, sufficient conditions for this type of operator are also discussed.

2

High-order fractional partial differential equation transform for molecular surface construction

100%

Hu L. , Chen D. , Wei G.-W.

Molecular Based Mathematical Biology

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2013

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tom 1

1-25

EN

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

3

On a class of analytic functions generated by fractional integral operator

100%

Ibrahim R. W.

Concrete Operators

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2017

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tom 4

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nr 1

1-6

EN

In this note, we improve the idea of the Tsallis entropy in a complex domain. This improvement is contingent on the fractional operator in a complex domain (type Alexander). We clarify some new classes of analytic functions, which are planned in view of the geometry function theory. This category of entropy is called fractional entropy; accordingly, we demand them fractional entropic geometry classes. Other geometric properties are established in the sequel. Our exhibition is supported by the Maxwell Lemma and Jack Lemma.

4

On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

100%

Baskonus H. M. , Bulut H.

Open Mathematics

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2015

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tom 13

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nr 1

EN

In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy of method used in this paper.

5

Fractional Hamilton’s equations of motion in fractional time

100%

Muslih S. , Baleanu D. , Rabei E.

Open Physics

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2007

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tom 5

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nr 4

549-557

EN

The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in fractional time. The fractional Hamilton’s equations are obtained and two examples are investigated in detail.

6

Monotonic solutions of multi term fractional differential equations

100%

Salem H. A. H.

Commentationes Mathematicae

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2007

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tom 47

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nr 1

EN

In this paper, we present an existence of monotonic solutions for a nonlinear multi term non-autonomous fractional differential equation in the Banach space of summable functions. The concept of measure of noncompactness and a fixed point theorem due to \(G\). Emmanuele is the main tool in carring out our proof.

7

Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

88%

Povstenko Y.

Open Mathematics

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2014

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tom 12

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nr 4

611-622

EN

The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.

8

Fractional virus epidemic model on financial networks

88%

Balci M. A.

Open Mathematics

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2016

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tom 14

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nr 1

1074-1086

EN

In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.

9

Third-order differential subordination and superordination involving a fractional operator

75%

Ibrahim R. W. , Ahmad M. Z. , Al-Janaby H. F.

Open Mathematics

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2015

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tom 13

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nr 1

EN

The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.