Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations And Applications

This book presents systematic coverage of fuzzy fractional differential equations and its applications to a variety of disciplines within engineering and the sciences. Complete with comprehensive results and solutions, the authors detail newly developed methods of fuzzy computational techniques needed to model solve uncertainty. Fuzzy logic differential equations are utilized via various analytical and numerical methodologies, and the book presents their importance for problem solving and prototype engineering design and systems testing. In recent years, modeling of differential equations for arbitrary and fractional order systems has been been increasing in its applicability, and as such, the book features examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to name a few. MATLAB is utilized to further illustrate the modeling of uncertain physical phenomena and problems in terms of non-probalistic methods as well as to facilitate easier understanding of the presented concepts. The fundamentals of fractional differential equations and the basic preliminaries of fuzzy fractional differential equations are first introduced, followed by numerical solutions, comparisons of various methods, and simulated results. In addition, fuzzy ordinary, partial, linear, and nonlinear fractional differential equations are addressed to solve uncertainty in physical systems.