Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles

Villamizar-Roa, Élder J.; Angulo-Castillo, Vladimir; Chalco-Cano, Y.

doi:10.1016/j.fss.2014.07.015

Cited by 39 publications

(15 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bede and Gal [85] presented a concept of generalized Hukuhara differentiability of fuzzy valued map-pings, which permits them to obtain the solutions of FDEs with a diminishing diameter of solutions values. This was followed up in the literature [85][86][87][88][89][90][91]. This comprehensive definition allows us to resolve the disadvantages of the previous fuzzy derivatives.…”

Section: Fuzzy Derivative and Solution Of Fuzzy Differentialmentioning

confidence: 99%

Different Solution Strategies for Solving Epidemic Model in Imprecise Environment

et al. 2018

View full text Add to dashboard Cite

We study the different solution strategy for solving epidemic model in different imprecise environment, that is, a Susceptible-Infected-Susceptible (SIS) model in imprecise environment. The imprecise parameter is also taken as fuzzy and interval environment. Three different solution procedures for solving governing fuzzy differential equation, that is, fuzzy differential inclusion method, extension principle method, and fuzzy derivative approaches, are considered. The interval differential equation is also solved. The numerical results are discussed for all approaches in different imprecise environment.

show abstract

Section: Fuzzy Derivative and Solution Of Fuzzy Differentialmentioning

confidence: 99%

Different Solution Strategies for Solving Epidemic Model in Imprecise Environment

et al. 2018

View full text Add to dashboard Cite

show abstract

“…Crisp Fuzzy EOQ EPQ Carbon FDE T2FS gH-differentiability emission Hovelaque and Bironneau [11] Battini et al [3] Jonas et al [12] Villamizar-Roa et al [36] Guchhait et al [10] Majumder et al [20] Shekarian et al [30] Kazemi et al [14] Proposed Model…”

Section: Authorsmentioning

confidence: 99%

Multi-objective Sustainable Fuzzy Economic Production Quantity (SFEPQ) Model with Demand as Type-2 Fuzzy Number: A Fuzzy Differential Equation Approach

Debnath¹,

Majumder²,

Bera³

2019

HJMS

View full text Add to dashboard Cite

A sustainable fuzzy economic production quantity (SFEPQ) inventory model is formulated by introducing the concept of fuzzy differential equation (FDE) due to dynamic behavior of the production-demand system. Generalized Hukuhara (gH) differentiability proceedure is applied to solve FDE. Since the demand parameter is taken as trapezoidal type-2 fuzzy number, to get corresponding defuzzified values, first critical value (CV)-based reduction method is applied on demand function to transfer into type-1 fuzzy variable which turns to hexagonal fuzzy number in form. After that α-cut of a hexagonal fuzzy number is used to find the upper and lower value of demand. To apply the α-cut operation on FDE, we divided the interval [0,1] into two sub-intervals [0,0.5] and [0.5,1] and gH-differentiation is applied on this sub-intervals. The objective of this paper is to maximize the profit and simultaneously minimize the carbon emission cost occurring due to the process of inventory management. Finally, the non-linear objective functions are solved by using of multi-objective genetic algorithm and sensitivity analyses on various parameters are also performed in numerically and graphically. Mathematics Subject Classification (2010). 90B05, 90B30

show abstract

“…Other researchers have proposed several approaches to the solutions of FDEs (e.g. [11][12][13][14], [15]). Almost authors applied the fixed point theorems like the Darbo's theorem and the classical Banach fixed point theorem [16], Schauder's fixed point theorem [17] and the method of successive approximations [8],.…”

Section: Introductionmentioning

confidence: 99%

“…Using Arzela-Ascoli's theorem and Schauder's fixed point theorem, authors proved thr existence and uniqueness of the solution for this kind ITM Web of Conferences 20, 02008 (2018) https://doi.org/10.1051/itmconf/20182002008 ICM 2018 of equations. In [14], using the contractive-like mapping principles, authors discussed the existence and uniqueness of solution of fuzzy differential equation under generalized Hukuhara derivative.…”

Section: Introductionmentioning

confidence: 99%

Application of Contractive-like Mapping Principles to Fuzzy Functional Differential Equation

2018

ITM Web Conf.

View full text Add to dashboard Cite

show abstract

Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles

Cited by 39 publications

References 34 publications

Different Solution Strategies for Solving Epidemic Model in Imprecise Environment

Different Solution Strategies for Solving Epidemic Model in Imprecise Environment

Multi-objective Sustainable Fuzzy Economic Production Quantity (SFEPQ) Model with Demand as Type-2 Fuzzy Number: A Fuzzy Differential Equation Approach

Application of Contractive-like Mapping Principles to Fuzzy Functional Differential Equation

Contact Info

Product

Resources

About