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, the tracking control of a class uncertain linear dynamical systems is investigated. The uncertainty considered to be represented as fuzzy numbers, and hence, these are referred systems, which presented in form differential equations (FDEs). solution an FDE found using approach called relative-distance-measure interval arithmetic under granular differentiability concept. objective ...

Let K be a closed convex cone with the nonempty interior in a real Banach space and cc(K) denote the family of all nonempty convex compact subsets of K. If {F t : t ≥ 0} is a concave iteration semigroup of continuous linear set-valued functions F t : K → cc(K) with F (x) = {x} for x ∈ K, then DtF (x) = F (G(x)) for x ∈ K and t ≥ 0, where DtF (x) denotes the Hukuhara derivative of F (x) with res...

Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We de...

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

The Hukuhara-Levelt-Turrittin decomposition theorem gives a classification of differential modules over the field C((z)) of formal Laurent series resembling the decomposition of a finite-dimensional vector space equipped with a linear endomorphism into generalized eigenspaces. It implies that after adjoining a suitable root of z, one can express any differential module as a successive extension...

This article introduces the concept of weak sharp minima for convex interval-valued functions. To solve constrained and unconstrained IOPs by WSM, we provide primal dual characterizations set WSM. The characterization is given in terms gH-directional derivatives. On other hand, to derive characterizations, propose notions support function a subset $$I({\mathbb {R}})^{n}$$ gH-subdifferentiabilit...

The present research correlates with a fuzzy hybrid approach merged homotopy perturbation transform method known as the Shehu (SHPTM). With aid of Caputo and Atangana–Baleanu under generalized Hukuhara differentiability, we illustrate reliability this scheme by obtaining fractional Cauchy reaction–diffusion equations (CRDEs) initial conditions (ICs). Fractional CRDEs play vital role in diffusio...

in this paper, a fuzzy hunter-saxton equation is solved by using the adomian'sdecomposition method (adm) and homotopy analysis method (ham). theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. the existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. a nume...