Exact and numerical solutions of sequential fractional differential equations of order in (1,2)

An exact continuous solution of a class of nonlinear two-term sequential fractional differential equations (SFDEs) is derived using the contraction principle. The solution is generated by the stationary function of the highest order derivative and exists in an arbitrary finite interval. For equations of order in (1; 2), the initial value problem (IVP) is also formulated and solved. The obtained analytical results are applied in the construction of a numerical scheme based on the transformation of an SFDE into an equivalent fractional integral equation. The numerical solutions are compared to the analytical ones in two cases. The errors are analyzed for a step size tending to 0 and the experimental order of convergence (EOC) is calculated in the included examples.