In this paper we present an efficient branch-following procedure that can be used not only to compute branches of periodic solutions of periodically forced dynamical systems but also to determine the stability of the periodic solutions. The procedure combines Broyden’s method with a subspace iteration method to determine the dominant eigenvalues. The method has connections with the hybrid Newto...

In this paper, we study the existence and uniqueness of Hadamard Itô-Doob Stochastic Fractional Order Systems (HIDSFOS) using Picard iteration method. Different from previous works, our paper presents a new theory fractional integral. We have proved convergence solution averaged HIDSFOS to that standard in sense mean square also probability. Some examples are given at end illustrate theoretical...

Hilfer fractional stochastic differential equations with delay are discussed in this paper. Firstly, the solutions to corresponding given using Laplace transformation and its inverse. Afterwards, Picard iteration technique contradiction method brought up demonstrate existence uniqueness of understanding, respectively. Further, finite-time stability is obtained generalized Grönwall–Bellman inequ...

In this paper, we show that for any finite order entire function $f(z)$, the function of the form $f(z)^{n}[f(z+c)-f(z)]^{s}$ has no nonzero finite Picard exceptional value for all nonnegative integers $n, s$ satisfying $ngeq 3$, which can be viewed as a different result on Hayman conjecture. We also obtain some uniqueness theorems for difference polynomials of entire functions sharing one comm...

We prove existence and uniqueness of a mild solution stochastic evolution equation driven by standard α-stable cylindrical Lévy process defined on Hilbert space for α∈(1,2). The coefficients are assumed to map between certain domains fractional powers the generator present in equation. is constructed as weak limit Picard iteration using tightness arguments. Existence strong obtained general ver...