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The world is grappled with an unprecedented challenges due to Corona virus. We are all battling this epidemic together, but we have not been able to defeat this epidemic yet. A new variant of this virus, named 'Omicron' is spreading these days. The fractional differential equations are providing us with better tools to study the mathematical model with memory effects. In this paper, we will consider an extended SER mathematical model with quarantined and vaccinated compartment to speculate the Omicron variant. This extended Susceptible Exposed Infected Recovered SER model involves equations that associate with the group of individuals those are susceptible (S), exposed (E): this class includes the individuals who are infected but not yet infectious, infectious (W): this class includes the individuals who are infected but not yet Quarantined, quarantined (Q): this class includes those group of people who are infectious, confirmed and quarantined, recovered (R) this class includes the group of individuals who have recovered, and vaccinated (V): this class includes the group of individuals who have been vaccinated. The non-negativity and of the extended SER model is analysed, the equilibrium points and the basic reproduction number are also calculated. The proposed model is then extended to the mathematical model using AB derivative operator. Proof for the existence and the uniqueness for the solution of fractional mathematical model in sense of AB fractional derivative is detailed and a numerical method is detailed to obtain the numerical solutions. Further we have discussed the efficiency of the vaccine against the Omicron variant via graphical representation. [ABSTRACT FROM AUTHOR]

We present iteration formulae of a fractional space-time telegraph equation using the combination of fractional variational iteration method and local fractional Laplace transform. [ABSTRACT FROM AUTHOR]

In this paper we solve generalized fractional differential equations by using the Sumudu transform. The equations solved differential equations with generalized Riemann-Liouville fractional derivative operators are very general in nature and involve wide range of fractional differential equations and their solutions in terms of various functions related to Mittag - Leffler function. [ABSTRACT FROM AUTHOR]

This paper presents a new method to solve the local fractional partial differential equations (LFPDEs) describing fractal vehicular traffic flow. Firstly, the existence and uniqueness of solutions to LFPDEs were proved and then two schemes known as the basic method (BM) and modified local fractional variational iteration method (LFVIM) were developed to solve the local fractional PDEs. Multiple studies have been reported in the literature to solve these problems using iterative methods which are time‐consuming and prone to errors. For linear problems, basic method was found highly accurate and computationally sound. We derived a modified version of LFVIM to investigate and obtain the nondifferentiable solutions of linear, nonlinear, and nonhomogeneous LFPDEs arising in fractal vehicular traffic flow through illustrative examples. Study results show that both schemes are very effective and can be used successfully to solve fractal vehicular traffic flow problems. [ABSTRACT FROM AUTHOR]

In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are considered as convergent series with easily computable components. Also, the obtained solutions have simplicity procedure, high accuracy and efficient. [ABSTRACT FROM AUTHOR]

This paper aims to solve general fractional Lane-Emden-Fowler differential equations using the Haar wavelet collocation method. This method transforms the fractional differential equation into a nonlinear system of equations, which is further solved for Haar coefficients using Newton's method. We have constructed the higher-order Lane-Emden-Fowler equations. We have also discussed the convergence rate and stability analysis of our technique. We have explained the applications and numerically simulated the examples graphically and in tabular format to elaborate on the accuracy and efficiency of this approach. [ABSTRACT FROM AUTHOR]