University of GuilanJournal of Mathematical Modeling2345-394X11120230301Second order spline method for fractional Bagley-Torvik equation with variable coefficients and Robin boundary conditions117132612610.22124/jmm.2022.23040.2047ENJoe Christin MarySDepartment of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, IndiaAyyaduraiTamilselvanDepartment of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, IndiaJournal Article20221010A fractional Bagley-Torvik equation of variable coefficients with Robin boundary conditions is considered in this paper. We prove the existence of the solution which is demonstrated by converting the boundary value problem into a Volterra integral equation of the second kind and also prove the uniqueness of the solution by using the minimum principle. We propose a numerical method that combines the second order spline approximation for the Caputo derivative and the central difference scheme for the second order derivative term. Meanwhile, the Robin boundary conditions is approximated by three-point endpoint formula. It is to be proved that this method is of second order convergent. Numerical examples are provided to demonstrate the accuracy and efficiency of the method.https://jmm.guilan.ac.ir/article_6126_547b7620438b0ea28a7de272cd09f1be.pdf