An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

Figure 5

Approximation 𝑥₂(𝑡) to the exact solution 𝑥(𝑡)=𝑡 of the fractional problem of the calculus of variations (54)-(55), obtained from the application of Theorem 7 and the classical Pontryagin maximum principle, that is, obtained by solving (67)-(68) with 𝑁=2.