Fuzzy differential equations and applications for engineers and scientists (Q2832133)

The book focuses on the basics of fuzzy set theory with preliminaries on fuzzy differential equations. It deals with various analytical and numerical methods to solve fuzzy differential equations subject to fuzzy initial or boundary conditions.NEWLINENEWLINEThe first chapter describes the basics of fuzzy set theory such as fuzzy numbers, types of fuzzy numbers, double parametric form of fuzzy number and fuzzy arithmetic concepts. The second chapter presents the basics of fuzzy and fuzzy fractional differential equations using Caputo-type fuzzy fractional derivatives. The third chapter examines some analytical methods for \(n\)-th order fuzzy differential equations, namely, fuzzy centre-based method, method based on addition and subtraction of fuzzy numbers, fuzzy centre and fuzzy radius-based method and double parametric-based method. All these methods are illustrated by simple mathematical examples and application problems.NEWLINENEWLINEIn Chapter 4, some numerical methods like Euler, improved Euler, collocation and the Galerkin-type are discussed to find the solution of fuzzy differential equations. Further semianalytical methods such as homotopy perturbation method, Adomian decomposition method and variational iteration method are also implemented to solve fuzzy initial value problems. The fifth chapter discuses the methods given in Chapter 4 for solving fuzzy ordinary differential equations. The obtained results are compared with the exact solutions.NEWLINENEWLINEIn Chapter 6, uncertain fuzzy partial differential equation is converted to an interval fuzzy differential equation using the single parametric form of fuzzy numbers. It is again transformed to a crisp differential equation using double parametric form of fuzzy numbers. Finally, it is solved by using homotopy perturbation and Adomian decomposition methods.NEWLINENEWLINEThe seventh chapter deals with the solution procedure to handle vibration of circular membranes. Homotopy perturbation method and Adomian decomposition method are applied to obtain the solutions of vibration equations of large membranes. The main advantage of these methods is the capability to achieve exact solutions and rapid convergence with few terms.NEWLINENEWLINEChapter 8 explains the uncertain rate of burning trees by solving fuzzy hyperbolic reaction-diffusion equations with different uncertain initial conditions which are considered in terms of trapezoidal and Gaussian convex normalized fuzzy sets. The obtained results may give an idea for how to handle the uncertain forest fire.NEWLINENEWLINEChapter 9 investigates an uncertain inverse heat conduction problem. Double parametric-based uncertain inverse heat conduction problem is solved with help of variational iteration method. In the final Chapter 10, the double parametric form of fuzzy numbers along with the homotopy perturbation method has been applied to solve the fuzzy fractional Klein-Gordon equation with uncertain initial conditions.NEWLINENEWLINEThis precisely written book covers the basic concepts of fuzzy ordinary and partial differential equations. The recent methods for solving fuzzy differential equations along with important application problems are discussed. Sufficient references are given at the end of each chapters and a small index is given which ends the volume. This book is worthy and can be recommended for graduate, post graduate students and teachers/researchers who work with uncertain dynamical systems.