Abstract
In this chapter, we investigate the variable-order fractional derivatives with singular kernels. We main present the concepts of the Riemann–Liouville-type variable-order fractional integrals and derivatives with singular kernel, variable-order Hilfer-type fractional derivatives with singular kernel, Liouville–Weyl-type variable-order fractional integrals and derivatives with singular kernel, as well as Riesz- Feller-, and Herrmann-type variable-order fractional derivatives with singular kernel.
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