Numerical solution of the fractional Bagley-Torvik equation by using hybrid functions approximation (Q2786701)

Using the relations between the Caputo fractional derivative and Riemann-Liouville fractional integral operator, the authors find the approximate solutions of the Cauchy problem and the boundary value problem for the differential equation of fractional order NEWLINE\[NEWLINE A D^{2}f(t)+ B D^{3/2}f(t) + C f(t)= g(t) NEWLINE\]NEWLINE on the interval \([0,1]\) with the constant coefficients \( A,B,C \). The approximate solution of these problems is presented as the following combination NEWLINE\[NEWLINE f(t)= \sum^{M}_{m=0}\sum^{N}_{n=1}c_{mn}b_{mn}(t),NEWLINE\]NEWLINE where \( b_{mn}(t)\) is a system of functions based on the Bernoulli polynomials. For three given illustrative examples the approximate and exact solutions are equal and have the form of polynomials.