The department has the exclusive jurisdiction of granting certificates of public convenience and necessity for the operation of common carriers by air for the transportation of persons or property. Upon the filing of an application for a certificate of public convenience and necessity, the department shall, within a reasonable time, fix a time and place for hearing the application, not less than twenty (20) days after the filing, and shall hear and determine the application within a reasonable length of time. If the department finds that the proposed operation is justified, and that the applicant is fit, willing and able to properly perform the services proposed and to conform to this chapter and the requirements, rules and regulations of the department, it shall issue a certificate to the applicant, subject to the terms, limitations and restrictions the department may deem proper, authorizing in whole or in part the operation covered by the application. If the department finds that the proposed operation is not justified, the application shall be denied. At the time an application is filed, the department shall require the payment of an application fee, which shall be set by the department at an amount sufficient to defray the usual costs of a hearing. Nothing in this section in any way applies to an air carrier operating by authority of a certificate, or certificates, of public convenience and necessity issued by the civil aeronautics authority, the civil aeronautics board, or any other federal agency authorized to issue such certificates.