In this paper, we study semi-analytical methods entitled Homotopy pertourbation method (HPM) to solve fuzzy impulsive fractional differential equations based on the concept of generalized Hukuhara differentiability. At the end first of Homotopy pertourbation method is defined and its properties are considered completely. Then econvergence theorem for the solution are proved and we will show tha...

In this work we present a new class of numerical semigroups called GSI-semigroups. We see the relations between them and others families give explicitly their set gaps. Moreover, an algorithm to obtain all GSI-semigroups up given Frobenius number is provided realization positive integers as numbers studied.

This paper focuses on the differentiability properties of the control-to-state mapping for entropy solutions to a scalar hyperbolic conservation law on R with respect to the switching times of an on/off control. As an example we consider the traffic density on a unidirectional road described by the LWR-model that is controlled by a traffic light switching between red and green at certain times....

In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. ...

This article studies continuity and differentiability properties for a reformulation of a finite-dimensional quasi-variational inequality (QVI) problem using a regularized gap function approach. For a special class of QVIs, this gap function is continuously differentiable everywhere, in general, however, it has nondifferentiability points. We therefore take a closer look at these nondifferentia...

Peano differentiability is a notion of higher order differentiability in the ordinary sense. H. W. Oliver gave sufficient conditions for the mth Peano derivative to be a derivative in the ordinary sense in the case of functions of a real variable. Here we generalize this theorem to functions of several variables.

space. For ( ) 1 h L X ∈ ,Γ,μ and Z∈Γ with indicator function ( ) Z I L X ∞ ∈ ,Γ, , μ the integral Z h ∫ dμ will be denoted by Z h I , . Now, we shall define the notion of differentiability for n-set functions. Morris [7] introduced differentiability for set functions and Corley [4] defined this notion for n -set functions. A function : Γ→ φ ! is said to be differentiable at T if there exists (...