New properties of the switching points for the generalized Hukuhara differentiability and some results on calculus

2021 ◽  
Vol 404 ◽  
pp. 62-74
Author(s):  
Y. Chalco-Cano ◽  
T.M. Costa ◽  
H. Román-Flores ◽  
A. Rufián-Lizana
Keyword(s):  
Generalized Hukuhara Differentiability

scholarly journals Fuzzy Volterra Integro-Differential Equations Using General Linear Method

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 381 ◽  
Author(s):  
Zanariah Abdul Majid ◽  
Faranak Rabiei ◽  
Fatin Abd Hamid ◽  
Fudziah Ismail
Keyword(s):  
Differential Equations ◽  
Lagrange Interpolation ◽  
Linear Method ◽  
Interpolation Polynomial ◽  
General Linear ◽  
Kutta Method ◽  
Lagrange Interpolation Polynomial ◽  
Runge Kutta Method ◽  
General Linear Method ◽  
Generalized Hukuhara Differentiability

In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalues of a multisteps method. The derivation of general linear method is based on the theory of B-series and rooted trees. Here, the fuzzy general linear method using the approach of generalized Hukuhara differentiability and combination of composite Simpson’s rules together with Lagrange interpolation polynomial is constructed for numerical solution of fuzzy volterra integro-differential equations. To illustrate the performance of the method, the numerical results are compared with some existing numerical methods.

scholarly journals Novel Analysis of Fuzzy Physical Models by Generalized Fractional Fuzzy Operators

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Mohammed Kbiri Alaoui ◽  
F. M. Alharbi ◽  
Shamsullah Zaland
Keyword(s):  
Initial Conditions ◽  
Dynamical Behavior ◽  
Physical Models ◽  
Hybrid Technique ◽  
Gas Dynamics Equations ◽  
Transform Method ◽  
Unknown Quantity ◽  
Fuzzy Solution ◽  
Generalized Hukuhara Differentiability ◽  
The Given

The present article correlates with a fuzzy hybrid technique combined with an iterative transformation technique identified as the fuzzy new iterative transform method. With the help of Atangana-Baleanu under generalized Hukuhara differentiability, we demonstrate the consistency of this method by achieving fuzzy fractional gas dynamics equations with fuzzy initial conditions. The achieved series solution was determined and contacted the estimated value of the suggested equation. To confirm our technique, three problems have been presented, and the results were estimated in fuzzy type. The lower and upper portions of the fuzzy solution in all three examples were simulated using two distinct fractional orders between 0 and 1. Because the exponential function is present, the fractional operator is nonsingular and global. It provides all forms of fuzzy solutions occurring between 0 and 1 at any fractional-order because it globalizes the dynamical behavior of the given equation. Because the fuzzy number provides the solution in fuzzy form, with upper and lower branches, fuzziness is also incorporated in the unknown quantity. It is essential to mention that the projected methodology to fuzziness is to confirm the superiority and efficiency of constructing numerical results to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

scholarly journals On Fuzzy Improper Integral and Its Application for Fuzzy Partial Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
ElHassan ElJaoui ◽  
Said Melliani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transforms ◽  
Partial Differential ◽  
First Order ◽  
Improper Integral ◽  
Linear Partial Differential Equations ◽  
Riemann Integrals ◽  
Generalized Hukuhara Differentiability

We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

2019 ◽  
Vol 53 (3) ◽  
pp. 867-886
Author(s):  
Mehrdad Ghaznavi ◽  
Narges Hoseinpoor ◽  
Fatemeh Soleimani
Keyword(s):  
Multiobjective Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Order Relation ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

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