Vineet K. Srivastava

Analytical approximations of two and three dimensional time-fractional telegraphic equation by reduced differential transform method

Abstract In this article, an analytical solution based on the series expansion method is proposed to solve the time-fractional telegraph equation (TFTE) in two and three dimensions using a recent and reliable semi-approximate method, namely the reduced differential transformation method (RDTM) subjected to the appropriate initial condition. Using RDTM, it is possible to find exact solution or a closed approximate solution of a differential equation. The accuracy, efficiency, and convergence of the method are demonstrated through the four numerical examples.

Two-dimensional time fractional-order biological population model and its analytical solution

Abstract In this article, a mathematical model has been developed for the generalized time fractional–order biological population model (GTFBPM). The fractional derivative has been described in the Caputo sense. The model has been solved by a recent approximate analytic method so called the fractional reduced differential transform method (FRDTM). Using this method, it is possible to find the exact solution as well as closed approximate solution of a differential equation. Three numerical examples of GTFBPM have been provided in order to check the effectiveness, accuracy and convergence of the method. The special advantage of using this computational technique is that it is very easy to implement and takes small size of computation contrary to other numerical methods while dealing complex and tedious physical problems arising in various branches of natural sciences and engineering.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

The telegraph equation and its solution by reduced differential transform method

One-dimensional second-order hyperbolic telegraph equation was formulated using Ohms law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM). Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

Viscous potential flow analysis of electroaerodynamic instability of a liquid sheet sprayed with an air stream

The instability of a thin sheet of viscous and dielectric liquid moving in the same direction as an air stream in the presence of a uniform horizontal electric field has been carried out using viscous potential flow theory. It is observed that aerodynamic-enhanced instability occurs if the Weber number is much less than a critical value related to the ratio of the air and liquid stream velocities, viscosity ratio of two fluids, the electric field, and the dielectric constant values. Liquid viscosity has stabilizing effect in the stability analysis, while air viscosity has destabilizing effect.