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Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators

100%

Ahmad J., Mohyud-Din S. T., Srivastava H. M., Yang X.-J.

Waves, Wavelets and Fractals

2015

tom 1

nr 1

In this paper we develop analytical solutions for the Helmholtz and Laplace equations involving local fractional derivative operators. We implement the local fractional decomposition method (LFDM) for finding the exact solutions. The iteration procedure is based upon the local fractional derivative sense. The numerical results, whichwe present in this paper, show that the methodology used provides an efficient and simple tool for solving fractal phenomena arising in mathematical physics and engineering. Several illustrative examples are also provided.

On the controllability of fractional dynamical systems

100%

Balachandran K., Kokila J.

International Journal of Applied Mathematics and Computer Science

2012

tom 22

nr 3

523-531

This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

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

88%

Povstenko Y.

Open Mathematics

2014

tom 12

nr 4

611-622

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.

Ograniczanie wyników

1 International Journal of Applied Mathematics and Computer Science

1 Open Mathematics

1 Waves, Wavelets and Fractals

1 Ahmad J.

1 Balachandran K.

1 Kokila J.

1 Mohyud-Din S. T.

1 Povstenko Y.

1 Srivastava H. M.

1 Yang X.-J.

1 2015

1 2014

1 2012

Wyniki wyszukiwania

Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators

On the controllability of fractional dynamical systems

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