In this article, we find the solution of time-fractional Belousov–Zhabotinskii reaction by implementing two well-known analytical techniques. The proposed methods are the modified form of the Adomian decomposition method and homotopy perturbation method with Yang transform. In Caputo manner, the fractional derivative is used. The solution we obtained is in the form of series which helps in investigating the analytical solution of the time-fractional Belousov–Zhabotinskii (B-Z) system. To verify the accuracy of the proposed methods, an illustrative example is taken, and through graphs, the solution is shown. Also, the fractional-order and integer-order solutions are compared with the help of graphs which are easy to understand. It has been verified that the solution obtained by using the given approaches has the desired rate of convergence to the exact solution. The proposed technique’s principal benefit is the low amount of calculations required. It can also be used to solve fractional-order physical problems in a variety of domains.

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This paper is concerned with the application of the variational principle to nonlinear oscillators with fractional power. In the proposed approach, high-order trial solutions are assumed with unknown parameters that are estimated using conditions by the variational theory. To perform integration in the proposed approach, linearization of the nonlinear term is carried out for simple calculation. The proposed approach delivered an estimate of the oscillator frequency with a relative error as small as 0.009%.

Abstract:We use Ruscheweyh derivative to define certain new classes of analytic functions with bounded radius rotation and related to conic domains. Some interesting and significant results such as inclusion results, growth rate of coefficients and radius problems for these new classes of k-uniformly functions. Several special cases are discussed. Results obtained in this paper may stimulate further research activities in this field.

In this paper, a reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection has been considered. We have compared the solutions of stochastic and deterministic typhoid fever model. It has been shown that the stochastic typhoid fever model is more realistic as compared to the deterministic typhoid fever model. The effect of threshold number T * hold in stochastic typhoid fever model. The proposed framework of the stochastic non-standard finite difference scheme (SNSFD) preserves all dynamical properties like positivity, bounded-ness and dynamical consistency defined by Mickens, R. E. The stochastic numerical simulation of the model showed that increase in protection leads to low disease prevalence in a population.