Fractional kinetic equations involving generalized k-Bessel function via Sumudu transform

A study on fractional differential equations using the fractional Fourier transform

“…There are many advantages of Hyers-Ulam type stability in tackling problems, related to optimization techniques, numerical analysis, control theory, and many more. Further advances in the Hyers-Ulam stability of differential equation can be found in [23][24][25][26][27][28][29][30][31][32][33].…”

New Extension of Beta Function and Its Applications

“…The kinetic equations especially describe the continuity of motion of substance. The extension and generalization of fractional kinetic equations involving many fractional operators were found in [18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

On the p-k-Mittag-Leffler function

“…The kinetic equation has been studied starting from the previous generalization and considering different functions f , in particular, special functions and generalizations of them (see, for example [16], [20], [1], and the references in them)…”

“…Many authors have generalized differential equations (integral equations) by replacing the ordinary derivative (integral) by some of the definitions that contemplate non-integers; for example: Riemann-Liouville, Caputo, Grundwald-Letnikov, Hadamard and other more modern ones such as Caputo-Fabrizio (see e.g. [22], [2], [12], [24], [20], [1], and the references in them). In the solution of such differential (integral) equations the Mittag-Leffler function naturally appears to play a role analogous to that of the exponential function in the ordinary case.…”