Modeling and numerical analysis of fractional-order Bloch equations

Numerical simulation of the fractional Bloch equations

In physics and chemistry, specifically in NMR (nuclear magnetic resonance) or MRI (magnetic resonance imaging), or ESR (electron spin resonance) the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = (Mx,My,Mz) as a function of time when relaxation times T1 and T2 are present. Recently, some fractional models have been proposed for the Bl...

Numerical and Analytical Treatment of Differential Equations of Fractional Order

Presentation of two models for the numerical analysis of fractional integro-differential equations and their comparison

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

Transient chaos in fractional Bloch equations

The Bloch equation provides the fundamental description of nuclear magnetic resonance(NMR) and relaxation(T1 andT2). This equation is the basis for both NMR spectroscopy andmagnetic resonance imaging (MRI). The fractional-order Bloch equation is a generalizationof the integer-order equation that interrelates the precession of the x, y and z componentsof magnetization wit...

Numerical Simulations for Variable-order Fractional Nonlinear Delay Differential Equations

In this paper numerical studies for the variable-order fractional delay differential equations are presented. Adams-Bashforth-Moulton algorithm has been extended to study this problem, where the derivative is defined in the Caputo variable-order fractional sense. Special attention is given to prove the error estimate of the proposed method. Numerical test examples are presented to demonstrate u...