where we understand that y is a function of an independent variable t . (We use t because in many examples the independent variable happens to be time, but of course any other variable could be used. In current versions of Maple, the dependence of y on t must be explicit, i.e., one must write y(t).) It is sometimes convenient to use informal notation and refer to this example as y′ = 0 (a physi...

The present paper is concerned with semilinear partial differential equations involving a particular pseudo-differential operator. It investigates both fractal conservation laws and non-local HamiltonJacobi equations. The idea is to combine an integral representation of the operator and Duhamel’s formula to prove, on the one side, the key a priori estimates for the scalar conservation law and t...

in this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy fredholmintegro-differential equation of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

in this paper, the stability and boundedness of solutions of a second order nonlinear vectordifferential equation are investigated. our results include and improve some well-known results in therelevant literature.

In this paper, we investigate the controllability of first order linear fuzzy differential systems. We use direct construction method to derive results for three types controlled systems via (c1)-solution and (c2)-solution, respectively. An example is presented illustrate our theoretical results.

In this paper, we introduce a computational method to find an approximate analytical solution for fuzzy differential equations. At first, variational iteration method (VIM) is used to solve the crisp problem then with the extension principle we find the fuzzy approximation solution. Examples are given , including linear and nonlinear fuzzy firstorder differential equations.

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...