scholarly journals Controllability of Sobolev type fuzzy differential equation with non-instantaneous impulsive condition

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Muslim Malik ◽  
Anjali Rose ◽  
Anil Kumar
Keyword(s):  
Differential Equation ◽  
Fuzzy Differential Equation ◽  
Sobolev Type ◽  
Impulsive Condition

Revisiting albedo from a fuzzy perspective

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Morteza Pakdaman ◽  
Majid Habibi Nokhandan ◽  
Yashar Falamarzi
Keyword(s):  
Differential Equation ◽  
Energy Balance ◽  
Fuzzy Number ◽  
Climate Models ◽  
Energy Balance Model ◽  
Fuzzy Differential Equation ◽  
Balance Model ◽  
Content Type ◽  
Fuzzy Energy ◽  
Fuzzy Derivative

PurposeThe aim of this paper is to revisit the albedo for uncertainty. The albedo is considered as a fuzzy value due to some realistic reasons which they will be discussed in details. After defining an appropriate uncertain albedo by using fuzzy set theory, the related energy balance model is also redefined as a fuzzy differential equation by using the concept of fuzzy derivative.Design/methodology/approachThe well-known Earth energy balance model is redefined as a fuzzy differential equation by using the concept of fuzzy derivative. Thus, instead of an ordinary differential equation, a fuzzy differential equation arises which it's solution procedure will be discussed in details.FindingsResults indicate that the fuzzy uncertainty for albedo causes more real results after solving the fuzzy energy balance equation. Considering albedo as a fuzzy number is more realistic than considering a single certain number for albedo of a surface. This is due to this fact that the Earth's surface coverage is not crisp and the boundaries of different types of lands are not consistent. The proposed approach of this paper can help us to provide more realistic climate models and construct dynamical models which can model the albedo based on its variability.Originality/valueIn this paper, we defined fuzzy energy balance model as a fuzzy differential equation for the first time. We also, considered albedo as a fuzzy number which is another novel approach.

scholarly journals Existence and uniqueness theorem for a solution of fuzzy differential equations

1999 ◽  
Vol 22 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Jong Yeoul Park ◽  
Hyo Keun Han
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of A Solution

By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equationx′(t)=f(t,x(t)),x(t0)=x0. We also consider anϵ-approximate solution of the above fuzzy differential equation.

Stability in credibility for fuzzy differential equation

2019 ◽  
Vol 36 (1) ◽  
pp. 213-218
Author(s):  
Cuilian You ◽  
Yangyang Hao ◽  
Ke Su
Keyword(s):  
Differential Equation ◽  
Fuzzy Differential Equation

scholarly journals ON LAGUERRE–SOBOLEV TYPE ORTHOGONAL POLYNOMIALS: ZEROS AND ELECTROSTATIC INTERPRETATION

2013 ◽  
Vol 55 (1) ◽  
pp. 39-54
Author(s):  
LUIS ALEJANDRO MOLANO MOLANO
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Inner Product ◽  
Sobolev Type ◽  
Electrostatic Model ◽  
Order Linear Differential Equation ◽  
Standard Methods ◽  
Linear Differential ◽  
Electrostatic Interpretation ◽  
Image Position

AbstractWe study the sequence of monic polynomials orthogonal with respect to inner product $$\begin{eqnarray*}\langle p, q\rangle = \int \nolimits \nolimits_{0}^{\infty } p(x)q(x){e}^{- x} {x}^{\alpha } \hspace{0.167em} dx+ Mp(\zeta )q(\zeta )+ N{p}^{\prime } (\zeta ){q}^{\prime } (\zeta ),\end{eqnarray*}$$ where $\alpha \gt - 1$, $M\geq 0$, $N\geq 0$, $\zeta \lt 0$, and $p$ and $q$ are polynomials with real coefficients. We deduce some interlacing properties of their zeros and, by using standard methods, we find a second-order linear differential equation satisfied by the polynomials and discuss an electrostatic model of their zeros.

Sign in / Sign up

Export Citation Format

Share Document