Symmetrization of diagonalizable complex differential systems

Complex fuzzy linear systems

Oscillatory properties of complex differential systems

Let A(z) be an nxn matrix whose elements are analytic functions of a complex variable z in a simply-connected domain D. The differential equation is said to be nonoscillatory in D if it does not possess a nontrivial solution vector w = (w-,. . • ,w ) such that w(z,) = 0, k = l,.,.,n, where the z^ are points of D. Ihe equation is called suborthogonal in D if, for any z, £ e D and any nontrivial ...

Diagonalization of non-diagonalizable discrete holomorphic dynamical systems

We shall describe a canonical procedure to associate to any (germ of) holomorphic self-map F of C fixing the origin so that dFO is invertible and non-diagonalizable an n-dimensional complex manifold M , a holomorphic map π:M → C, a point e ∈ M and a (germ of) holomorphic self-map F̃ of M such that: π restricted to M \ π(O) is a biholomorphism between M \ π(O) and C \ {O}; π ◦ F̃ = F ◦ π; and e is...

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

Simultaneous preconditioning and symmetrization of non-symmetric linear systems

Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations [6, 7], we propose new templates for solving large non-symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well known iterative methods for solving linea...