In this article, the active control method is used for hybrid synchronization between two fractional order hyperchaotic systems, Chen hyperchaotic system taken as the master system and the other fractional order hyperchaoticLu system taken as slave system separately. The fractional derivative is described in Caputo sense. Numerical simulation results which are carried out using Adams–Bashforth–...

This paper introduces techniques for the estimation of solutions to fractional order differential equations (FODEs) and the approximation of a function’s Caputo fractional derivative. These techniques are based on scattered data interpolation via reproducing kernel Hilbert spaces (RKHSs). Specifically, an RKHS is generated for the purpose of estimating fractional derivatives from the Mittag-Lef...

In this paper we analyse the stability of weak discrete stationary shocks. The difference approximation is conservative, dissipative and k-th order accurate (k = 1 or k = 3). In Sections 1-3, following the previous results of D. Michelson we adapt the multistep methods RungeKutta and Adams-Bashforth to solve systems of conservation laws. In section 4 we analyse the stability of the numerical me...

A recently proposed numerical scheme for solving nonlinear ordinary differential equations with integer and non-integer Liouville-Caputo derivative is applied to three systems chaotic solutions. The Adams-Bashforth involving Lagrange interpolation the fundamental theorem of fractional calculus. We provide existence uniqueness solutions, also convergence result state...

In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM was utilized establish approximate series solutions. technique considered be an extension original Adams–Bashforth–Moulton approach. Numerical simulations and figures are discussed, in order show efficiency of proposed method. futur...

Surface tension is a meaningful parameter influencing boiling and condensation in macroscopic scale, confined spaces, or for nanofluids; it further affects with surfactants. Surface, interfacial, an important property the research into increasing heat transfer, enhancing efficiency of photovoltaic systems, improving engine operation, forming drugs polymers. It often determined using axisymmetri...

Implicit-explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave, slow-wave problems in which the fast wave is physically insignificant and need not be accurately simulated. The widely used combination of trapezoidal implicit and leapfrog explicit differencing is compared to schemes based on 5 Adams methods or on backward differen...

Transient stability-constrained optimal power flow (TSCOPF) models comprehensively analyze the security and economic operation of systems. However, they require a high computational effort can suffer from convergence problems when applied to large This study analyzes performance eleven numerical integration algorithms ordinary differential equations that represent system dynamics in TSCOPF mode...