Numerical solution of fuzzy delay differential equations under generalized differentiability by Euler's method

In this paper, we interpret a fuzzy delay differential equations using the concept of generalized differentiability. Using the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. The Euler approximation method is implemented and its error analysis is discussed. The applicability of the theoretical results is illustrated with some examples

Fuzzy Calculus with Noval Approach Using Fuzzy Functions

This article deals with the complexity involved in fuzzy derivatives when both input and output are from nonempty, convex, and compact fuzzy space. Consider a fuzzy valued mapping, and for fuzzy differentiation of fuzzy valued function, we propose Modified Hukuhara derivative. To evaluate this derivative, we need to take the parametric form of, input and the mapping which is involved in it. Our definition gives a more realistic explanation of fuzzy derivatives, under this derivative, we also develop fuzzy Taylor series along with its convergence. Lastly, we solve a fully fuzzy differential equation with initial condition using Fuzzy Taylor series.Comment: 22 pages, 1 figur

Comparisons of the exact and the approximate solutions of second-order fuzzy linear boundary value problems

WOS: 000504461100014In this paper, the approximate solutions by using the undetermined fuzzy coefficients method and the exact solutions by using the Hukuhara differentiability of second-order fuzzy linear boundary value problems with constant coefficients are investigated. Thus, comparisons of the found solutions are given

Efficient approximate analytical methods for nonlinear fuzzy boundary value problem

This paper aims to solve the nonlinear two-point fuzzy boundary value problem (TPFBVP) using approximate analytical methods. Most fuzzy boundary value problems cannot be solved exactly or analytically. Even if the analytical solutions exist, they may be challenging to evaluate. Therefore, approximate analytical methods may be necessary to consider the solution. Hence, there is a need to formulate new, efficient, more accurate techniques. This is the focus of this study: two approximate analytical methods-homotopy perturbation method (HPM) and the variational iteration method (VIM) is proposed. Fuzzy set theory properties are presented to formulate these methods from crisp domain to fuzzy domain to find approximate solutions of nonlinear TPFBVP. The presented algorithms can express the solution as a convergent series form. A numerical comparison of the mean errors is made between the HPM and VIM. The results show that these methods are reliable and robust. However, the comparison reveals that VIM convergence is quicker and offers a swifter approach over HPM. Hence, VIM is considered a more efficient approach for nonlinear TPFBVPs

Numerical Solution of Fuzzy Arbitrary Order Predator-Prey Equations

This paper seeks to investigate the numerical solution of fuzzy arbitrary order predator-prey equations using the Homotopy Perturbation Method (HPM). Fuzziness in the initial conditions is taken to mean convex normalised fuzzy sets viz. triangular fuzzy number. Comparisons are made between crisp solution given by others and fuzzy solution in special cases. The results obtained are depicted in plots and tables to demonstrate the efficacy and powerfulness of the methodology