39,790 research outputs found
On Some Linear and Non-linear Fuzzy Integral Equations by Homotopy Perturbation Method
Many mathematical models are contributed to give rise to of linear and nonlinear integral equations. In this paper, we study the performance of recently developed technique homotopy perturbation method by implement on various types of linear and non-linear fuzzy Volterra integral equations of second kind, mixed fuzzy volterra fredholm integral equation and singular fuzzy integral equations. Obtained results show that technique is reliable, efficient and easy to use through recursive relations that involve integrals. Moreover, these particular examples show the reliability and the performance of proposed modifications. Keywords: Homotopy perturbation method, linear fuzzy integral equations, non-linear fuzzy integral equations
Fuzzy Stochastic Differential Equations Driven by Semimartingales-Different Approaches
The first aim of the paper is to present a survey of possible approaches for the study of fuzzy stochastic differential or integral equations. They are stochastic counterparts of classical approaches known from the theory of deterministic fuzzy differential equations. For our aims we present first a notion of fuzzy stochastic integral with a semimartingale integrator and its main properties. Next we focus on different approaches for fuzzy stochastic differential equations. We present the existence of fuzzy solutions to such equations as well as their main properties. In the first approach we treat the fuzzy equation as an abstract relation in the metric space of fuzzy sets over the space of square integrable random vectors. In the second one the equation is interpreted as a system of stochastic inclusions. Finally, in the last section we discuss fuzzy stochastic integral equations with solutions being fuzzy stochastic processes. In this case the notion of the stochastic ItĂŽâs integral in the equation is crisp; that is, it has single-valued level sets. The second aim of this paper is to show that there is no extension to more general diffusion terms
On the Lp-spaces techniques in the existence and uniqueness of the fuzzy fractional Korteweg-de Vries equationâs solution
In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on LP-spaces are used, defining the LpF F ([0; 1]) for 1â€Pâ€â, its properties, and using the functional analysis methods. Also the convergence of the method of successive approximations used to approximate the solution of fuzzy integral equation be proved and an iterative procedure to solve such equations is presented
HÀgusad teist liiki integraalvÔrrandid
KÀesolevas doktoritöös on uuritud hÀgusaid teist liiki integraalvÔrrandeid. Need vÔrrandid sisaldavad hÀgusaid funktsioone, s.t. funktsioone, mille vÀÀrtused on hÀgusad arvud.
Me tĂ”estasime tulemuse sileda tuumaga hĂ€gusate Volterra integraalvĂ”rrandite lahendite sileduse kohta. Kui integraalvĂ”rrandi tuum muudab mĂ€rki, siis integraalvĂ”rrandi lahend pole ĂŒldiselt sile. Nende vĂ”rrandite lahendamiseks me vaatlesime kollokatsioonimeetodit tĂŒkiti lineaarsete ja tĂŒkiti konstantsete funktsioonide ruumis. Kasutades lahendi sileduse tulemusi tĂ”estasime meetodite koonduvuskiiruse.
Me vaatlesime ka nĂ”rgalt singulaarse tuumaga hĂ€gusaid Volterra integraalvĂ”rrandeid. Uurisime lahendi olemasolu, ĂŒhesust, siledust ja hĂ€gusust. Ălesande ligikaudseks lahendamiseks kasutasime kollokatsioonimeetodit tĂŒkiti polĂŒnoomide ruumis. TĂ”estasime meetodite koonduvuskiiruse ning uurisime lĂ€hislahendi hĂ€gusust. Nii analĂŒĂŒs kui ka numbrilised eksperimendid nĂ€itavad, et gradueeritud vĂ”rke kasutades saame parema koonduvuskiiruse kui ĂŒhtlase vĂ”rgu korral.
Teist liiki hĂ€gusate Fredholmi integraalvĂ”rrandite lahendamiseks pakkusime uue lahendusmeetodi, mis pĂ”hineb kĂ”igi vĂ”rrandis esinevate funktsioonide lĂ€hendamisel TĆĄebÔƥovi polĂŒnoomidega. Uurisime nii tĂ€pse kui ka ligikaudse lahendi olemasolu ja ĂŒhesust. TĂ”estasime meetodi koonduvuse ja lĂ€hislahendi hĂ€gususe.In this thesis we investigated fuzzy integral equations of the second kind. These equations contain fuzzy functions, i.e. functions whose values are fuzzy numbers.
We proved a regularity result for solution of fuzzy Volterra integral equations with smooth kernels. If the kernel changes sign, then the solution is not smooth in general. We proposed collocation method with triangular and rectangular basis functions for solving these equations. Using the regularity result we estimated the order of convergence of these methods.
We also investigated fuzzy Volterra integral equations with weakly singular kernels. The existence, regularity and the fuzziness of the exact solution is studied. Collocation methods on discontinuous piecewise polynomial spaces are proposed. A convergence analysis is given. The fuzziness of the approximate solution is investigated. Both the analysis and numerical methods show that graded mesh is better than uniform mesh for these problems.
We proposed a new numerical method for solving fuzzy Fredholm integral equations of the second kind. This method is based on approximation of all functions involved by Chebyshev polynomials. We analyzed the existence and uniqueness of both exact and approximate fuzzy solutions. We proved the convergence and fuzziness of the approximate solution.https://www.ester.ee/record=b539569
H ? filtering for stochastic singular fuzzy systems with time-varying delay
This paper considers the H? filtering problem
for stochastic singular fuzzy systems with timevarying
delay. We assume that the state and measurement
are corrupted by stochastic uncertain exogenous
disturbance and that the system dynamic is modeled
by Ito-type stochastic differential equations. Based on
an auxiliary vector and an integral inequality, a set of
delay-dependent sufficient conditions is established,
which ensures that the filtering error system is e?t -
weighted integral input-to-state stable in mean (iISSiM).
A fuzzy filter is designed such that the filtering
error system is impulse-free, e?t -weighted iISSiM and
the H? attenuation level from disturbance to estimation
error is belowa prescribed scalar.Aset of sufficient
conditions for the solvability of the H? filtering problem
is obtained in terms of a new type of Lyapunov
function and a set of linear matrix inequalities. Simulation
examples are provided to illustrate the effectiveness
of the proposed filtering approach developed in
this paper
Classical dynamics on three dimensional fuzzy space: Connecting the short and long length scales
We derive the path integral action for a particle moving in three dimensional
fuzzy space. From this we extract the classical equations of motion. These
equations have rather surprising and unconventional features: They predict a
cut-off in energy, a generally spatial dependent limiting speed, orbital
precession remarkably similar to the general relativistic result, flat velocity
curves below a length scale determined by the limiting velocity and included
mass, displaced planar motion and the existence of two dynamical branches of
which only one reduces to Newtonian dynamics in the commutative limit. These
features place strong constraints on the non-commutative parameter and
coordinate algebra to avoid conflict with observation and may provide a
stringent observational test for this scenario of non-commutativity.Comment: 21 pages, 4 figure
Choquet Integral of Fuzzy-Number-Valued Functions: The Differentiability of the Primitive with respect to Fuzzy Measures and Choquet Integral Equations
This paper deals with the Choquet integral of fuzzy-number-valued functions based on the nonnegative real line. We firstly give the definitions and the characterizations of the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on the nonadditive measure. Furthermore, the operational schemes of above several classes of integrals on a discrete set are investigated which enable us to calculate Choquet integrals in some applications. Secondly, we give a representation of the Choquet integral of a nonnegative, continuous, and increasing fuzzy-number-valued function with respect to a fuzzy measure. In addition, in order to solve Choquet integral equations of fuzzy-number-valued functions, a concept of the Laplace transformation for the fuzzy-number-valued functions in the sense of Choquet integral is introduced. For distorted Lebesgue measures, it is shown that Choquet integral equations of fuzzy-number-valued functions can be solved by the Laplace transformation. Finally, an example is given to illustrate the main results at the end of the paper
Comparison for accurate solutions of nonlinear Hammerstein fuzzy integral equations
In this paper, efficient numerical techniques have been proposed to solve nonlinear Hammerstein fuzzy integral equations. The proposed methods are based on Bernsteinpolynomials and Legendre wavelets approximation. Usually, nonlinear fuzzy integral equations are very difficult to solve both analytically and numerically. The present methods applied to the integral equations is reduced to solve the system of nonlinear algebraic equations. Again, this system has been solved by Newtonâs method. The numerical results obtained by present methods have been compared with those of the homotopy analysis method. Illustrative examples have been discussed to demonstrate the validity and applicability of the presented methods
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