In this work we develop a theory of fractional stimulated Raman adiabatic passage (FSTIRAP) using frequency-chirped pulses (CFSTIRAP). We analyze the CFSTIRAP as a method to create a coherent superposition state maximizing coherence between the initial and the target state in the presence of the two-photon detuning. We demonstrate that the pulse chirping permits relaxation of the condition of the two-photon resonance required for adiabatic passage in STIRAP and FSTIRAP. The choice of the chirp rate enables adiabatic passage to a predetermined state between two nearly degenerate final states within a broad range of values of the two-photon detuning and the chirp rate. The proposed schemes will expand the scope of quantum control methods and contribute to the further improvement of quantum imaging, sensing, and metrology.