On differentiability of solutions of fractional differential equations with respect to initial data

In this paper, we deal with a Cauchy problem for nonlinear fractional differential equation the Caputo derivative of order $$\alpha \in (0, 1)$$ . As initial data, consider pair consisting an point, which does not necessarily coincide inferior limit derivative, and function that determines values solution on interval from to point. We study differentiability properties functional associating data endpoint corresponding problem. Stimulated by recent results dynamic programming principle Hamilton–Jacobi–Bellman equations optimal control problems, examine so-called coinvariant derivatives $$ functional. prove these exist give formulas their calculation.