TY - JOUR ID - 6126 TI - Second order spline method for fractional Bagley-Torvik equation with variable coefficients and Robin boundary conditions JO - Journal of Mathematical Modeling JA - JMM LA - en SN - 2345-394X AU - S, Joe Christin Mary AU - Tamilselvan, Ayyadurai AD - Department of Mathematics, Bharathidasan University, Tiruchirappalli - 620 024, Tamilnadu, India Y1 - 2023 PY - 2023 VL - 11 IS - 1 SP - 117 EP - 132 KW - Fractional Bagley-Torvik equation KW - Caputo fractional derivative KW - Robin boundary conditions KW - spline method KW - convergence Analysis DO - 10.22124/jmm.2022.23040.2047 N2 - A 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. UR - https://jmm.guilan.ac.ir/article_6126.html L1 - https://jmm.guilan.ac.ir/article_6126_547b7620438b0ea28a7de272cd09f1be.pdf ER -