Iterative Method Applied to the Fractional Nonlinear Systems Arising in Thermoelasticity With Mittag-Leffler Kernel

Numerical Methods Partial

et al. 2020

Throughout the globe, mankind is in vastly infected situations due to a cruel and destructive virus called coronavirus (COVID‐19). The pivotal aim of the present investigation is to analyze and examine the evolution of COVID‐19 in India with the available data in two cases first from the beginning to 31st March and beginning to 23rd April in order to show its exponential growth in the crucial period. The present situation in India with respect to confirmed, active, recovered and deaths cases have been illustrated with the aid of available data. The species of novel virus and its stages of growth with respect some essential points are presented. The exponential growth of projected virus by the day‐to‐day base is captured in two‐dimensional plots to predict its developments and identify the needs to control its spread on mankind. Moreover, the SEIR model is considered to present some interesting consequences about COVID‐19 within the frame of fractional calculus. A newly proposed technique called q‐Homotopy analysis transform method (q‐HATM) is hired to find the solution for the nonlinear system portraying projected model and also presented the existence and uniqueness of the obtained results with help of fixed point theory. The behavior has been captured with respect to fractional order and time. The present study exemplifies the importance of fractional operator and efficiency of the projected algorithm.

Section: Mathematical Formulation and Analysismentioning

confidence: 99%

A mathematical analysis of ongoing outbreakCOVID‐19 in India through nonsingular derivative

Safare¹,

Betageri²,

Numerical Methods Partial

et al. 2020

“…Since q-HATM is an improved scheme of HAM; it does not require discretization, perturbation or linearization. Recently, due to its reliability and e cacy, the considered method is exceptionally applied by many researchers to understand physical behaviour diverse classes of complex problems [45][46][47][48][49][50][51][52][53]. The projected method o ers us more freedom to consider the diverse class of initial guess and the equation type complex as well as nonlinear problems; because of this, the complex NDEs can be directly solved.…”

Section: Introductionmentioning

confidence: 99%

A reliable analytical technique for fractional Caudrey-Dodd-Gibbon equation with Mittag-Leffler kernel

Veeresha

2020

Nonlinear Engineering

Self Cite

The pivotal aim of the present work is to find the solution for fractional Caudrey-Dodd-Gibbon (CDG) equation using q-homotopy analysis transform method (q-HATM). The considered technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the projected fractional-order model. In order to illustrate and validate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of q-HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The obtained results elucidate that, the considered algorithm is easy to implement, highly methodical as well as accurate and very effective to examine the nature of nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

“…The theory of derivative with non‐integer order has been improved because of the difficulties linked to the phenomenon with heterogeneities. The fractional differential equations are more noticeable nowadays due to their exceptional applications in the field of scientific discipline and engineering like fluid and continuum mechanics [7], electrodynamics [8], chaos theory [9], finance [10], biological population models [11], signal processing [12] and many more [13–33], which are well explained by non‐integer order differential equations. Regrettably, it has been very complicated to find precise solutions to nonlinear fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

An efficient computational technique for time‐fractionalKaup‐Kupershmidtequation

Numerical Methods Partial

Malagi

Veeresha

et al. 2020

In this article, an efficient novel technique, namely the q‐homotopy analysis transform method (q‐HATM) is applied to find the solution for the time‐fractional Kaup‐Kupershmidt (KK) equation. The KK equation plays a vital role while studying the capillary gravity waves and nonlinear dispersive waves. To check the effectiveness and pertinency of the projected method, we consider three distinct cases of the fractional nonlinear KK equation. The q‐HATM provides the auxiliary parameter ℏ, called convergence control parameter, with the help of that we can manipulate and adjust the area of convergence of the series solution. Moreover, to authenticate the accuracy and reliability of the considered technique the numerical simulations have been presented. The retrieved results ensure that the projected scheme is effortless to carry out and analyze the highly nonlinear problems arising in science and technology.