| Volume 14, Number 6, 2024, Pages - DOI：10.11948/JAAC-2024-0079 |
| Properties of a new generalized Caputo-Fabrizio fractional derivative |
| Marc Jornet,Juan José Nieto |
| Keywords:fractional calculus fractional derivative fractional integral operator nonsingular kernel |
| Abstract: |
| We investigate properties of a new fractional derivative recently introduced in the literature, which aims at generalizing the well-known Caputo-Fabrizio operator. We study the null space of the generalized derivative, the associated fractional integral operator, the null space of this integral, the validity of a fundamental theorem of calculus, the equivalence of integral problems with ordinary differential equations, the existence and uniqueness of solution for integral problems, and the form the nonsingular kernel should have to ensure consistency with the fractional order. A complete example with power input function is analyzed, which gives rise to a novel non-elementary solution and new dynamics in terms of the famous Lambert function. |
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