Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

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Some generalized fractional calculus operators and their applications in integral equations (2012, methodology): “In [9], the authors investigate a Caputo type modification of the Erdélyi-Kober fractional derivative.”
Existence and Uniqueness results for a class of Generalized Fractional Differential Equations (2014, background): “The interested reader may find Caputo-type modification of the Erdélyi-Kober fractional derivative in the works of Luchko [20].”
A BRIEF STORY ABOUT THE OPERATORS OF THE GENERALIZED FRACTIONAL CALCULUS (2008, methodology): “[12] A. Kilbas, H.M. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations.”
A Caputo fractional derivative of a function with respect to another function (2016, methodology): “For some special cases of ψ, we obtain the Caputo fractional derivative [25], the Caputo–Hadamard fractional derivative [12, 15] and the Caputo–Erdélyi–Kober fractional derivative [18].”
Fractional derivatives and the fundamental theorem of fractional calculus (2020, background): “Thus, the many parameters families of the fractional integrals and derivatives (say, the Erdélyi-Kober operators [19, 38] or their Caputo type modifications [20,28]), the distributed order fractional derivatives [5, 6, 21,24], the fractional derivatives with the general kernels [22, 39, 40], and the”