k -Fractional Integrals and Application

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On the k-Riemann-Liouville fractional integral and applications (2014, background): “,( )( )()( yx yx k k kkyxB Later, under these definitions, Mubeen and Habibullah (2012) have introduced thek -fractional intregral of the Riemann-Liouville type as follows: .0,0,0,)( )( 1 )( 1 0 kxdttftxk xfJ k x k k Note that when ,1k then it reduces to the classical…”
On Pólya–Szegö and Čebyšev type inequalities via generalized k-fractional integrals (2020, background): “Now, we recall the definition of k-fractional integral [88].”
(k, s)-Riemann-Liouville fractional integral and applications (2016, background): “Later, under the above definitions, in [13], Mubeen and Habibullah have introduced the k-fractional integral of the Riemann-Liouville type as follows: kJ f(x) = 1 kΓk(α) ∫ x”