Solving evolution equations using a new iterative method

In this article, we apply the new iterative method proposed by Daftardar‐Gejji and Jafari (J Math Anal Appl 316, (2006), 753–763) for solving various linear and nonlinear evolution equations. The results obtained are compared with the results by existing methods. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Theory of gel filtration chromatography. Elution patterns of solutes in the presence of micellar and premicellar aggregates of micelle-forming surfactants

The theory presented prevously by us (J. Am. Chem. Soc., 100 (1978) 5914) of Gel Filtration Chromatography (GFC) with varying concentration of the aqueous surfactant solutions and fixed solute concentration has been augmented. The rationalisation of our GFC results with the CTAB surfactant solutions and Co(cydta)^– on the Sephadex G-25 fine columns demanded the postulation of the premicellar aggregate formation. The GFC theory has been worked out using these observations. Four different distinguished possibilities in the realm of the premicellar aggregation have been investigated. The use of the equations so developed for the elution patterns of the solutes with negative and positive adsorption on the gel matrix has been discussed. Moreover, the presence of the premicellar aggregates in the imbibed phase beyond the usual CMC modifies the relevant GFC expression originally derived by Herries, Bishop and Richards (J. Phys. Chem., 68 (1964) 1842).     

Boundary value problems for multi-term fractional differential equations

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.     

An Iterative method for solving fractional differential equations

In the present paper non-linear, time fractional advection partial differential equation has been solved using the new iterative method presented by Daftardar-Gejji and Jafari [1]. The results are compared with those obtained by Adomian decomposition and Homotopy perturbation methods. It is demonstrated that the new iterative method gives the best approximation among these. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics analysis of fractional order Yu-Wang system

Fractional order version of a dynamical system introduced by Yu and Wang (Engineering, Technology & Applied Science Research, 2, (2012) 209–215) is discussed in this article. The basic dynamical properties of the system are studied. Minimum effective dimension 0.942329 for the existence of chaos in the proposed system is obtained using the analytical result. For chaos detection, we have calculated maximum Lyapunov exponents for various values of fractional order. Feedback control method is then used to control chaos in the system. Further, the system is synchronized with itself and with fractional order financial system using active control technique. Modified Adams-Bashforth-Moulton algorithm is used for numerical simulations.     

Synthesis of crystalline umangite phase of copper selenide (Cu3Se2) for TiO2 photoanode-based solar cell application

Journal of Solid State Electrochemistry - This study deals with the sensitization of the porous titanium oxide (TiO2) films deposited on fluorine doped tin oxide with copper selenide (Cu3Se2). The...     

Nonexistence of invariant manifolds in fractional-order dynamical systems

Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in planar polynomial systems. We provide the conditions for the invariance of linear subspaces in fractional-order systems. Further, we provide an important result showing the nonexistence of invariant manifolds (other than linear subspaces) in fractional-order systems.