Approximation of solution for generalized Basset equation with finite delay using Rothe's approach

Abstract

This study focuses on the use of the Riemann-Liouville fractional (R-L) derivative to address an initial boundary value problem for a fractional order differential equation with finite delay (FDDE). Rothe's methodology is used to prove the existence and uniqueness of the strong solution and classical solution to the restated abstract FDDE. Some examples based on abstract theory and numerical solutions of FDDEs arising in fluid dynamics are presented.