A New Generalized Definition of Fractional Derivative with Non-Singular Kernel

Abstract

This paper proposes a new definition of fractional derivative with non-singular kernel in the sense of Caputo which generalizes various forms existing in the literature. Furthermore, the version in the sense of Riemann–Liouville is defined. Moreover, fundamental properties of the new generalized fractional derivatives in the sense of Caputo and Riemann–Liouville are rigorously studied. Finally, an application in epidemiology as well as in virology is presented.

Keywords

• fractional derivative
• non-singular kernel
• Mittag–Lefler function
• fractional differential equations
• epidemiology