scholarly journals GENERAL SOLUTION OF BASSET EQUATION WITH CAPUTO GENERALIZED HUKUHARA DERIVATIVE

2016 ◽  
Vol 6 (1) ◽  
pp. 119-130
Author(s):  
A. Armand ◽  
◽  
T. Allahviranloo ◽  
Z. Gouyandeh
Keyword(s):  
General Solution ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative

scholarly journals A New Method to Find Fuzzy Nth Order Derivation and Applications to Fuzzy Nth Order Arithmetic Based on Generalized H-Derivation

2014 ◽  
Vol 4 (2) ◽  
pp. 105-121
Author(s):  
Laleh Hooshangian ◽  
Tofigh Allahviranloo
Keyword(s):  
Differential Equations ◽  
New Method ◽  
Order Derivative ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Order Arithmetic ◽  
Order Derivation

In this paper, fuzzy nth-order derivative for n in N is introduced. To do this, nth-order derivation under generalized Hukuhara derivative here in discussed. Calculations on the fuzzy nth-order derivative on fuzzy functions and their relationships, in general, are introduced. Then, the fuzzy nth-order differential equations is solved, for n in N.

A novel difference and derivative of linearly correlated fuzzy number-valued functions

2022 ◽  
pp. 1-17
Author(s):  
Yonghong Shen
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Hukuhara Difference ◽  
Interval Numbers ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Generalized Hukuhara Difference ◽  
Interval Valued

In the present paper, the notion of the linearly correlated difference for linearly correlated fuzzy numbers is introduced. Especially, the linearly correlated difference and the generalized Hukuhara difference are coincident for interval numbers or even symmetric fuzzy numbers. Accordingly, an appropriate metric is induced by using the norm and the linearly correlated difference in the set of linearly correlated fuzzy numbers. Based on the symmetry of the basic fuzzy number, the linearly correlated derivative is proposed by the linearly correlated difference of linearly correlated fuzzy number-valued functions. In both non-symmetric and symmetric cases, the equivalent characterizations of the linearly correlated differentiability of a linearly correlated fuzzy number-valued function are established, respectively. Moreover, it is shown that the linearly correlated derivative is consistent with the generalized Hukuhara derivative for interval-valued functions.

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

2018 ◽  
Vol 20 ◽  
pp. 02008
Author(s):  
Vu Ho
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Functional Differential

In this paper, we prove the existence and uniqueness of solution for the fuzzy functional differential equation under generalized Hukuhara derivative via contractive-like mapping principles.

Calculus for interval-valued functions using generalized Hukuhara derivative and applications

2013 ◽  
Vol 219 ◽  
pp. 49-67 ◽  
Author(s):  
Y. Chalco-Cano ◽  
A. Rufián-Lizana ◽  
H. Román-Flores ◽  
M.D. Jiménez-Gamero
Keyword(s):  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Interval Valued

The Role of VLBI in the Establishment of Coordinate Systems

1975 ◽  
Vol 26 ◽  
pp. 293-295 ◽  
Author(s):  
I. Zhongolovitch
Keyword(s):  
General Solution ◽  
Future Development ◽  
Rational Approach ◽  
Radio Telescopes ◽  
Coordinate Systems ◽  
Tectonic Plates ◽  
Astronomical Observations ◽  
Optical Instruments ◽  
Fundamental Polyhedron

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

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