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Fractional calculus is a new branch of analytical mathematics which provides useful tools to model many physical and biological phenomena and optimal control of complex processes with memory effects. Therefore, new advancement of fractional calculus theory will greatly promote the development of function space theory, functional theory, and mathematical physics as well as their applications in differential and integral equations. This special issue mainly focuses on the latest achievements anddoi:10.1155/2019/5719808 fatcat:mwdi7rybjvabjot56zpesc6f7a