A New Iterative Predictor-Corrector Algorithm for Solving a System of Nuclear Magnetic Resonance Flow Equations of Fractional Order

Mariam Sultana,Heba Y. Zahran,Wedad Albalawi,Muhammad Khalid,Ali Akgül,Uroosa Arshad

doi:10.3390/fractalfract6020091

Abstract

Nuclear magnetic resonance flow equations, also known as the Bloch system, are said to be at the heart of both magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) spectroscopy. The main aim of this research was to solve fractional nuclear magnetic resonance flow equations (FNMRFEs) through a numerical approach that is very easy to handle. We present a New Iterative Predictor-Corrector Algorithm (NIPCA) based on the New Iterative Algorithm and Predictor-Corrector Algorithm to solve nonlinear nuclear magnetic resonance flow equations of fractional order involving Caputo derivatives. Graphical representation of the solutions with detailed error analysis shows the higher accuracy of the new technique. This New Iterative Predictor-Corrector Algorithm requires less computational time than previously published numerical methods. The results achieved in this article indicate that the algorithm is fit to use for other chaotic systems of fractional differential equations.

Highlights

Nuclear magnetic resonance provides the physical basis for a vast selection of methods that are usually used to investigate the dynamics of the structure of cells, tissues, etc., up to the extent of the entire body [1]
Chemists have recently studied biomolecules and their structural analysis using magnetic resonance spectroscopy (MRS), and magnetic resonance imaging (MRI) is a vital instrument in the radiology departments of hospitals
The typical means of defining nuclear magnetic resonance (NMR) (i.e., “the phenomena that make up the inner workings of MRI”) in vector form is presented with the help of the Bloch equation

Summary

Introduction

Nuclear magnetic resonance provides the physical basis for a vast selection of methods that are usually used to investigate the dynamics of the structure of cells, tissues, etc., up to the extent of the entire body [1]. The typical means of defining NMR (i.e., “the phenomena that make up the inner workings of MRI”) in vector form is presented with the help of the Bloch equation. This equation corresponding to a uniform sample may be expressed as [8,9]:. We present, for the first time, a new technique for the numerical solution of fractional nuclear magnetic resonance flow equations, in the form of the technique of the. A conclusive summary of the research is presented

Application on Fractional Nuclear Magnetic Resonance Flow Equations

Results and Discussion

When we consider

Approximate

Average absolute error

Conclusions