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...

The aim of this paper is to present some modifications of the biomorphs generation algorithm introduced by Pickover in 1986. A biomorph stands for biological morphologies. It is obtained by a modified Julia set generation algorithm. The biomorph algorithm can be used in the creation of diverse and complicated forms resembling invertebrate organisms. In this paper the modifications of the biomor...

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...

Abstract In recent years, researchers have studied the use of different iteration processes from fixed point theory in generation complex fractals. For instance, Mann, Ishikawa, Noor, Jungck–Mann and Jungck–Ishikawa iterations been used. this paper, we study Picard–Mann with s -convexity Mandelbrot Julia sets. We prove escape criterion for $$(k+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

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...