The generalized power fractional derivative operators with respect to another function in the kernel

Hira Khan, Gauhar Rahman, Muhammad Samraiz, Çetin Yildiz

Abstract


In this work, a new notion of the fractional derivatives with non-singular kernels the so-called power Caputo and Power Riemann-Liouville (R-L) operators associated with another function in the kernel are presented. The new defined operators are the generalization of different operators found in the literature. Some basic properties and formulas of the new operators are discussed. Additionally, novel formulas and properties of fractional derivatives and integrals in the Power Caputo and Power R-L senses are presented in this study. 


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DOI: https://doi.org/10.52846/ami.v52i2.2014