Utilizing the Caputo fractional derivative for the flux tube close to the neutral points

Abstract

This study examines how fractional derivatives affect the theory of curves and related surfaces, an application area that is expanding daily. There has been limited research on the geometric interpretation of fractional calculus. The present study applied the Caputo fractional calculation method, which has the most suitable structure for geometric computations, to examine the effect of fractional calculus on differential geometry. The Caputo fractional derivative of a constant is zero, enabling the geometric solution and understanding of many fractional physical problems. We examined flux tubes, which are magnetic surfaces that incorporate these lines of magnetic fields as parameter curves. Examples are visualized using mathematical programs for various values of Caputo fractional analysis, employing theory-related examples. Fractional derivatives and integrals are widely utilized in various disciplines, including mathematics, physics, engineering, biology, and fluid dynamics, as they yield more numerical results than classical solutions. Also, many problems outside the scope of classical analysis methods can be solved using the Caputo fractional calculation approach. In this context, applying the Caputo fractional analytic calculation method in differential geometry yields physically and mathematically relevant findings, particularly in the theory of curves and surfaces.