Fractional Differential Equations

Scattered Data Approximation

Most engineering and scientific phenomena, such as the surface of a landscape or the continuously changing temperature at a location are inherently infinite in space or time or both. We cannot measure all the data. Generally it is possible to record surface elevation values or the temperature only at some specific locations and times.

Interpolation and Approximation

Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

In this paper, we implement the radial basis functions for solving a classical type of time-fractional telegraph equation defined by Caputo sense for ð1oαr2Þ. The presented method which is coupled of the radial basis functions and finite difference scheme achieves the semi-discrete solution. We investigate the stability, convergence and theoretical analysis of the scheme which verify the validity of the proposed method. Numerical results show the simplicity and accuracy of the presented method. & 2013 Elsevier Ltd. All rights reserved.

Numerical solution of fractional telegraph equation by using radial basis functions

A new Wavelet Method for Variable‐Order Fractional Optimal Control Problems

Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion

The power transformer is one of the vital and substantial elements of each country's power grid which not only require high investment, but they are also important in terms of economy, social, political, and strategy. Since this equipment is exposed to different electrical and mechanical winding faults during operation, they should be monitored continuously. One of the main monitoring methods is the use of frequency response analysis (FRA), which has a high sensitivity. The main challenge of the FRA is that the detecting task of the status of the transformer is done by a specialist and with a visual evaluation of the records. To overcome this problem, first, frequency responses in the healthy and present states are calculated through simulation of electrical and mechanical fault in the winding of the transformer and then, new statistical methods are used to interpret FRA results based on the obtained transfer function. In this study, for the first time, clustering analysis and cross-correlation methods are used to interpret FRA results for clustering and diagnosis of different short circuits turns, axial displacement, and radial deformation. Results and simulations verify ability and advantage of these methods in detection and determination of different faults.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-gtd.2018.5812

Zakieh Avazzadeh

Papers

Numerical solution of fractional telegraph equation by using radial basis functions

A new Wavelet Method for Variable‐Order Fractional Optimal Control Problems

Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion

Diagnosis and clustering of power transformer winding fault types by cross-correlation and clustering analysis of FRA results

A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation