A reliable algorithm for fractional Bloch model arising in magnetic resonance imaging
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Magnetic resonance imaging (MRI) is used in physics, chemistry, engineering and medicine to study complex materials. In this paper, numerical solution of fractional Bloch equations in MRI is obtained using fractional variation iteration method (FVIM) and fractional homotopy perturbation transform method (FHPTM). Sufficient conditions for the convergence of FVIM and its error estimate are established. The obtained results are compared with the existing as well as recently developed methods and with the exact solution. The obtained numerical results for different fractional values of time derivative are discussed with the help of figures and tables. Figures are drawn using the Maple package. Test examples are provided to illustrate the accuracy and competency of the proposed schemes.
KeywordsFractional model of Bloch equations fractional variation iteration method magnetic resonance imaging Caputo fractional derivative fractional homotopy perturbation transform method
PACS Nos76.60.−k 87.19.Lf 87.10.Ed 02.60.Cb
The authors are thankful to the anonymous reviewers and editors for their valuable comments and suggestions to improve the quality of this paper.
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