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In this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. For its validity, an appropriate example is given.

Generalized Darbo-Type F-Contraction and F-Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation