In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is base...

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 article, we present a modified strategy that combines the residual power series method with Laplace transformation and novel iterative technique for generating solution to fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use Laurent in their development. new procedures’ advantages include accuracy speed obtaining exact/approximate solutions. suggested appro...

Models describing the plasma concentration-time curves of generated metabolite after iv and oral drug administration are presented. Utilizing numerical inverse Laplace transformation, the method can readily be used for parameter estimation and model simulation in conjunction with appropriate curve-fitting software. The approach is not limited to compartment modeling and can be applied to any li...

The numerical inverse Laplace transformation NILM makes use of numerical integration. Generally, a high-order scheme of numerical integration renders high accuracy. However, surprisingly, this is not true for the NILM to the transfer function. Numerical examples show that the performance of higher-order schemes is no better than that of the trapezoidal scheme. In particular, the solutions from ...

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A q-analogue of the ĝl3 Drinfel’d-Sokolov hierarchy is proposed as a reduction of the q-KP hierarchy. Applying a similarity reduction and a q-Laplace transformation to the hierarchy, one can obtain the q-Painlevé VI equation proposed by Jimbo and Sakai. AMS classification scheme numbers: 37K10, 39A12, 39A13 Submitted to: J. Phys. A: Math. Gen. Dedicated to Professors Junkichi Satsuma and Basil ...

The aim of this note is to give a straightforward proof of a general version of the Ciesielski-Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski-Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly a new transformation which maps a subset of the family of ...