Doddabhadrappla Gowda Prakasha

Bio: Doddabhadrappla Gowda Prakasha is an academic researcher from Davangere University. The author has contributed to research in topics: Laplace transform & Fractional calculus. The author has an hindex of 27, co-authored 88 publications receiving 1905 citations. Previous affiliations of Doddabhadrappla Gowda Prakasha include Karnatak University.

A homotopy technique for a fractional order multi-dimensional telegraph equation via the Laplace transform

Abstract: An effective analytical technique, called q-homotopy analysis transform method (q-HATM) is demonstrated in order to analyse a fractional model of telegraph equations. Test examples are illustrated to inspect the efficiency of the proposed technique. Numerical solutions are obtained in the form of series. Also, its convergence condition, error estimate and numerical simulation results are discussed. The q-HATM handles and controls a series solution that speedily converges to exact result in a small admissible domain efficiently.

Novel simulations to the time-fractional Fisher’s equation

Abstract: In the present work, an efficient numerical technique, called q-homotopy analysis transform method (briefly, $$q$$ -HATM), is applied to nonlinear Fisher’s equation of fractional order. The homotopy polynomials are employed, in order to handle the nonlinear terms. Numerical examples are illustrated to examine the efficiency of the proposed technique. The suggested algorithm provides the auxiliary parameters $$\hbar$$ and $$n$$ , which help us to control and adjust the convergence region of the series solution. The outcomes of the study reveal that the $$q$$ -HATM is computationally very effective and accurate to analyse nonlinear fractional differential equations.

New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach

Abstract: This manuscript investigates the fractional Phi-four equation by using q -homotopy analysis transform method ( q -HATM) numerically. The Phi-four equation is obtained from one of the special cases of the Klein-Gordon model. Moreover, it is used to model the kink and anti-kink solitary wave interactions arising in nuclear particle physics and biological structures for the last several decades. The proposed technique is composed of Laplace transform and q -homotopy analysis techniques, and fractional derivative defined in the sense of Caputo. For the governing fractional-order model, the Banach’s fixed point hypothesis is studied to establish the existence and uniqueness of the achieved solution. To illustrate and validate the effectiveness of the projected algorithm, we analyze the considered model in terms of arbitrary order with two distinct cases and also introduce corresponding numerical simulation. Moreover, the physical behaviors of the obtained solutions with respect to fractional-order are presented via various simulations.

A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative

Abstract: In this research, we aim to propose a new fractional model for human liver involving Caputo–Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard–Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives.

A new study of unreported cases of 2019-nCOV epidemic outbreaks

Abstract: 2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q-homotopy analysis transform method (q-HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.