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...

Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎The hybrid differential equations have a wide range of applications in science and engineering‎. ‎The hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎Hybrid fuzzy differential equations (HFDEs) is considered by ...