New Implementation of Residual Power Series for Solving Fuzzy Fractional Riccati Equation

This paper reveals a computational method using a Residual Power Series Method (RPSM) for the solution of fuzzy fractional riccati equation under caputo fractional differentiability. An analytical solution of fuzzy fractional riccati equation is obtained as a convergent fractional power series. The procedure produces solutions of high accuracy, and some illustrative examples are solved with a different value of orders to show the efficiency of the RPSM

Employment of Set Operations to Improve LMP Assessments Design and Implementation

Objective - This paper aims to provide a new mathematical model for the construction of assessment tools for Lean Manufacturing Practices (LMP) through the integration process with the set operations. This study also strives to develop key elements to enhance the effectiveness of LMP assessments and their impact through mathematical interrelationship.  Problem - Previous studies have shown a lack of clear mathematical methodology to carry out a rigorous assessment of the LMP effects on the firm’s operational and financial performance. Therefore, this paper tries to address this aspect by developing new equations.  Design - The methodology of this study is based on the conversion of the linguistic description (companies, processes, waste, practices) into numerical measurement model by integrating with set theory.  Finding - The results show a set of relationships and equations that can be applied to be a fundamental basis for ensuring the effectiveness of the assessment. This paper may contribute to the improvement of LMP’s design and development

Generalizing the meaning of derivatives and integrals of any order differential equations by fuzzy-order derivatives and fuzzy-order integrals

This paper develops the correlation between fuzzy numbers and order of differential equations and overcomes the limitation in the existence of fractional order in the formulation of equation. In the view of fractional calculus, a new logic called fuzzy order by generalizing the meaning of derivatives and integrals of any order as fuzzy-order derivatives and fuzzy-order integral. We discuss Dα, where Dα is derivative of order α and α may be a triangular fuzzy number or trapezoidal fuzzy number, and propose to rewrite Dαy(x)=gx,y(x), when α=A,B,C and A,BandC∈N (where N is the set of natural numbers) and rewrite Riemann-Liouville integral, Riemann-Liouville derivative and Caputo fractional derivatives with respect to this new logic of fuzzy order. The proposed approach also covers multi cases, where the order is either integer or fractional. At the end, three numerical examples are presented to demonstrate the application of new logic, when the order of derivatives and integrals are given as triangular fuzzy numbers. These include time fractional heat equation represented as a time fuzzy-order heat equation and the time-fractional diffusion wave equation represented as a time-fuzzy-order diffusion wave equation. Keywords: Fractional calculus, Fuzzy numbers, Riemann-Liouville fuzzy definitions, Caputo fuzzy definition