This paper addresses a new spectral collocation method for solving nonlinear fractional quadratic integral equations. The main idea of this method is to construct the approximate solution based on fractional order Chelyshkov polynomials (FCHPs). To this end, first, we introduce these polynomials and express some of their properties. The operational matrices of fractional integral and product are derived. The spectral collocation method is utilized together with operational matrices to reduce the problem to a system of algebraic equations. Finally, by solving this system, the unknown coefficients are computed. Further, the convergence analysis and numerical stability of the method are investigated. The proposed method is computationally simple and easy to implement in computer programming. The accuracy and applicability of the method is presented by some numerical examples.

The main aim of this paper is to construct a mathematical model for the spread of SARS-CoV-2 infection. We discuss the modified COVID-19 and change the model to fractional order form based on the Caputo-Fabrizio derivative. Also several definitions and theorems of fractional calculus, fuzzy theory and Laplace transform are illustrated. The existence and uniqueness of the solution of the model are proved based on the Banach's unique fixed point theory. Moreover Hyers-Ulam stability analysis is studied. The obtained results show the efficiency and accuracy of the model.

This article examines the oscillatory behaviour of solutions to a particular class of conformable elliptic partial differential equations of the Emden-Fowler type. Using the Riccati method, we create some new necessary conditions for the oscillation of all solutions. The previously discovered conclusions for the integer order equations are expanded upon by these additional findings. We provide an example to demonstrate the usefulness of our new finding.