Inverse problem for the Atangana-Baleanu fractional differential equation

In this manuscript, we examine a fractional inverse problem of order 0 < rho < 1 in a Banach space, including the Atangana-Baleanu fractional derivative in the Caputo sense. We use an overdetermined condition on a mild solution to identify the parameter. The major strategies for determining the outcome are a direct approach using the Volterra integral equation for sufficiently regular data. For less regular data, an optimal control approach uses Euler-Lagrange (EL) equations for the fractional order control problem (FOCP) and a numerical approach for solving FOCP. At last, a numerical example is provided in the support of our results.