Solving k-Fractional Hilfer Differential Equations via Combined Fractional Integral Transform Methods

In this paper, we introduce k-fractional Hilfer derivative given in [1]. A combination of fractional Fourier transform method and Laplace transform method is adopted to solve Cauchy-type problems involving k-fractional Hilfer derivatives and an integral operator whose kernel contains k-Mittag-Leffler function similar to the one given in [2]. The solutions to these problems are obtained in terms of Mittag-Leffler function.