In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solv...

We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and Green’s operators, we employ the algebra of integro-differential operators. The operations implemented for regular boundary problems include computing Green’s ...

This study is devoted to studying the existence and uniqueness of solutions for Hadamard implicit fractional differential equations with generalized integro-differential boundary conditions by utilizing contraction principle Banach Leray–Schauder fixed point theorems. Moreover, two different approaches, Hyers–Ulam stabilities are also discussed. Different ordinary third order (e.g., initial, an...

in this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. these results generalize the results of [17, 20] for differential inclusions with hukuhara derivative and of [18] for fuzzy differential equations.

The current research attempts to offer a novel method for solving fuzzy differential equations with initial conditions based on the use of feed-forward neural networks. First, the fuzzy differential equation is replaced by a system of ordinary differential equations. A trial solution of this system is written as a sum of two parts. The first part satisfies the initial condition and contains no ...

Abstract In this work, a technique for finding approximate solutions ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is hybrid between Galerkin and collocation methods. Also, can be extended to fractional integro-differential (FIDEs) optimal control problems (FOCPs). spatial approximations with their derivatives are based on shifted ultraspherical pol...

The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter enhances the uncertainty of the system reliability. In this paper, the concept of fuzzy reliability...

We construct the algebra of integro-differential operators over an ordinary integro-differential algebra directly in terms of normal forms. In the case of polynomial coefficients, we use skew polynomials for defining the integro-differential Weyl algebra as a natural extension of the classical Weyl algebra in one variable. Its normal forms, algebraic properties and its relation to the localizat...