On Boundary Value Problems for Second-order Fuzzy Linear Differential Equations with Constant Coefficients

In this paper we investigate the solutions of boundary value problems for second-order fuzzy linear differential equations with constant coefficients. There are four different solutions for the problems by using a generalized differentiability. Solutions and several comparison results are presented. Some examples are provided for which the solutions are found

A fractional multistep method for solving a class of linear fractional differential equations under uncertainty

The objective of this research has been devoted to solve linear fuzzy fractional differential equations (FFDEs) of the Caputo sense. The basic idea is to develop a fractional linear multistep method for solving linear FFDEs under fuzzy fractional generalized differentiability. For safely illustrating the advantages and potential of the presented method, a comparison with the fractional Euler method has to be analyzed in depth. We are interested in using a simple method to obtain gripping results

Review of modern numerical methods for a simple vanilla option pricing problem

Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication 20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515

A kernel least mean square algorithm for fuzzy differential equations and its application in earth's energy balance model and climate

Abstract This paper concentrates on solving fuzzy dynamical differential equations (FDDEs) by use of unsupervised kernel least mean square (UKLMS). UKLMS is a nonlinear adaptive filter which works by applying kernel trick to LMS adaptive filter. UKLMS estimates multivariate function which is embedded to estimate the solution of FDDE. Adaptation mechanism of UKLMS helps for finding solution of FDDE in a recursive scenario. Without any desired response, UKLMS finds nonlinear functions. For this purpose, an approximate solution of FDDE is constructed based on adaptable parameters of UKLMS. An optimization algorithm, optimizes the values of adaptable parameters of UKLMS. The proposed algorithm is applied for solving Earth energy balance model (EBM) which is considered as a fuzzy differential equation for the first time. The method in comparison with the other existing approaches (such as numerical methods) has some advantages such as more accurate solution and also that the obtained solution has a functional form, thus the solution can be obtained at each time in training interval. Low error and applicability of developed algorithm are examined by applying it for solving several problems. After comparing the numerical results, with relative previous works, the superiority of the proposed method will be illustrated