Legendre spectral method for the fractional Bratu problem

Abstract

In this paper, the Legendre spectral collocation method (LSCM) is applied for the solution of the fractional Bratu's equation. It shows the high accuracy and low computational cost of the LSCM compared with some other numerical methods. The fractional Bratu differential equation is transformed into a nonlinear system of algebraic equations for the unknown Legendre coefficients and solved with some spectral collocation methods. Some illustrative examples are also given to show the validity and applicability of this method, and the obtained results are compared with the existing studies to highlight its high efficiency and neglectable error.

Numerical computations and theoretical investigations of a dynamical system with fractional order derivative

“…Fractional order calculus have provided the information of the whole spectrum lying between any two different integer values [21] , [22] , [23] , [24] . The representation of various real problems have been modeled by fractional order differential or integral equation like, mathematical fractional order model for microorganism population, logistic non-linear model for human population, tuberculosis model, dingy problem, hepatitis B, C models and the basic Lotka-Volterra models being the basics of all infectious problems [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] . The afore said problems have been analyzed for qualitative analysis with help of some well known theorems of fixed point theory [35] , [36] , [37] , [38] , [39] .…”

Numerical simulation and stability analysis for the fractional-order dynamics of COVID-19

“…Aiming to propose a suitable dynamical system for the evolution of the pandemic spreading, in the following we propose a fractional-order dynamical model for the analysis of the virus spread, thereby showing that our model is best fitting with the available observations. Fractional calculus [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] has many real life applications. Here, we propose a scheme for solving the fractional-order corona virus model as suggested by Khan and Atangana [15] who presented the mathematical results of the model and then formulated a fractional-order model by using the Atangana-Baleanu fractional derivative.…”

Investigation of COVID-19 mathematical model under fractional order derivative

“…So for, many real world problems have been modeled by integer order differential equation, like population model,logistic equations, HIV, SEIR, HIV, Cancer model, Predator-prey model, etc. Further the scientists converted these equations to arbitrary order of differential equations which give much more real solution [26][27][28][29][30][31][32][33][34][35]. They have analyzed these equations for exitence and uniqueness by applying some of the properties and theorems of fixed point theory which is given in [36][37][38][39].…”