Certainly, here are some properties of the operator \(J^\rho\) (He 2000; Miller and Ross 1993), for \(\phi \in C_\lambda, \lambda \ge -1, \rho, \xi > 0\) listed as1
References
1Batool S, Arshad M, Perveen N, Sarwar S. Bright optical solution for fractional Lakshmanan–Porsezian–Daniel with spatio temporal dispersion by improved Adomian decomposition method. Optical and Quantum Electronics. 56(7):1137. doi:10.1007/s11082-024-07048-5