Fuzzy solution of system of fuzzy fractional problems using a reliable method

Abstract

Under uncertainty, the analytical behavior of fractional differential equations is frequently puzzling and difficult to predict. As a result, it's necessary to develop a suitable, comprehensive, and highly effective theory to solve these challenges. The fuzzy fractional differential equation theory is a relatively recent concept that has applications in engineering, applied mathematics. The fractional differential transform method (FDTM) is utilized in this study to determine the analytical fuzzy solution of some fuzzy fractional differential equations in Caputo sense, which are used to analyze a range of physical models in many sciences and engineering disciplines. The developed FFDE solutions are more generalized and have a wider range of applications. A parametric characterization of the solutions is obtained by converting the fuzzy fractional differential equation to an equivalent crisp system of corresponding fractional differential equations. The numerical and graphical presentation shows the symmetry between lower and upper cut representations of the fuzzy solutions and may be useful in better understanding of automatic control models, artificial intelligence, image classification, computer science, medical science, quantum optics, measure theory, physics, biology, optimal control theory, mathematical economics, and other domains, and non-financial analysis.

Keywords

• Fuzzy number
• Caputo fractional derivative
• Fractional differential transform method
• Fuzzy solution