Numerical Solutions for Fuzzy Fractional Differential Equations Using Logarithmic and Harmonic Means

Abstract

Fractional calculus is the study of the properties of integrals and derivatives of non-integer order. Fractional calculus evolved in the same way that classical calculus did. The concept of fractional differential equations is expected to improve a selection of real-world applications, including electrical circuits, biology, biomechanics, electrochemistry, and electromagnetic processes. Based on this the newly developed fractional differential equations have piqued the curiosity of mathematicians and their applications, to the point that they are currently used in engineering to describe a wide spectrum of physical and chemical processes. Understanding the qualitative and quantitative characteristics of complex physical phenomena necessitates the solution of nonlinear fractional differential equations in closed form (FDEs). Nonlinear themes include electrical engineering, mechanics, plasma physics, control theory, signal processing, finance, stochastic dynamical systems, and stochastic dynamical systems. In this study, we use a novel and extensible technique to analyse fuzzy fractional differential equations. The harmonic and logarithmic mean error investigations are extensive. The results demonstrate that this approach can solve fuzzy fractional differential equations precisely.