Elzaki residual power series method to solve fractional diffusion equation.

The time-fractional order differential equations are used in many different contexts to analyse the integrated scientific phenomenon. Hence these equations are the point of interest of the researchers. In this work, the diffusion equation for a one-dimensional time-fractional order is solved using a combination of residual power series method with Elzaki transforms. The residual power series approach is a useful technique for finding approximate analytical solutions of fractional differential equations that needs the residual function's (n-1)α derivative. Since it is challenging to determine a function's fractional-order derivative, the traditional residual power series method's application is somewhat constrained. The Elzaki transform with residual power series method is an attempt to get over the limitations of the residual power series method. The obtained numerical solutions are compared with the exact solution of this equation to discuss the method's applicability and efficiency. The results are also graphically displayed to show how the fractional derivative influences the behaviour of the solutions to the suggested method.

Soliton: A dispersion-less solution with existence and its types.

A solitary wave is the dispersion-less solution of nonlinear evolutionary equations that travels at a constant speed without dissipating its energy. The purpose of this article is to provide insight into the discovery and history of solitons. The different types of the solitons are discussed in brief that is helpful for the researchers. For the discussion of the nature of solitons, the solution behavior of the Korteweg de Vries equation (KdV), the sine-Gordon (SG), the Camassa-Holm (CH) equation, and the nonlinear Schrodinger (NLS) equation are considered. This article deals with the various applications of solitons in different fields such as biophysics, nonlinear optics, Bose-Einstein condensation, plasma physics, Josephson junction, etc. focusing on the properties of solitons based on their classification.

Numerical Simulation to Predict COVID-19 Cases in Punjab.

Coronavirus disease 2019 is a novel disease caused by a newly identified virus, Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). India recorded its first case of COVID-19 on 30 January 2020. This work is an attempt to calculate the number of COVID-19 cases in Punjab by solving a partial differential equation using the modified cubic B-spline function and differential quadrature method. The real data of COVID-19 cases and Google Community Mobility Reports of Punjab districts were used to verify the numerical simulation of the model. The Google mobility data reflect the changes in social behavior in real time and therefore are an important factor in analyzing the spread of COVID-19 and the corresponding precautionary measures. To investigate the cross-border transmission of COVID-19 between the 23 districts of Punjab with an analysis of human activities as a factor, the 23 districts were divided into five regions. This paper is aimed at demonstrating the predictive ability of the model.

Disseminated Nocardia nova infection.

We report the case of a 61-year-old female with ulcerative colitis on therapy with prednisone and azathioprine. The patient presented with fever, dry cough, a swollen lower extremity, and nodules on the right wrist and the scalp. Computed tomography scans of the head, chest, abdomen, and pelvis revealed multiple lesions. Aspirates and biopsies of the lower extremity cystic lesion, the wrist nodule, and the scalp nodule all grew out Nocardia nova. The patient was treated with high-dose trimethoprim and sulfamethoxazole therapy for one year and made a complete recovery.