fractional differential equations

Numerical solution for fractional differential equations by using Jacobi–Gauss–Radau collocation method

This study proposes a novel numerical approach for addressing both linear and nonlinear initial fractional order differential equations (FDEs) through the implementation of the Jacobi–Gauss–Radau (JGR) integrated with Caputo fractional derivatives.  The problem is effectively transformed into a simplified system of FDEs, encompassing the unknown coefficients, by employing shifted JGR points for the FDEs and their initial conditions.  For the purpose of investigating the effectiveness and accuracy of the introduced method, some numerical illustrations are provided for various linear and nonl

Stability analysis of a fractional model for the transmission of the cochineal

Scale insects are parasitic insects that attack many indoor and outdoor plants, including cacti and succulents.  These insects are among the frequent causes of diseases in cacti: for the reason that they are tough, multiply in record time and could be destructive to these plants, although they are considered resistant.  Mealybugs feed on the sap of plants, drying them out and discoloring them.  In this research, we propose and investigate a fractional model for the transmission of the Cochineal.  In the first place, we prove the positivity and boundedness of solutions i