On the properties of a Cauchy-type problem for an abstract differential equation with fractional derivatives

A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions

“…Now, Based on the composition in Lemma 24, in the next theorem we establish an equivalence with the following fractional integro-differential equation: (33)(34). We multiply (33) by (x -a) r to…”

“…Other physical and engineering processes are given in [31,32] In a series of articles, [33][34][35], Glushak studied the uniform well-posedness of a Cauchy-type problem with two fractional derivatives and bounded operator. He also proposed a criterion for the uniform correctness of unbounded operator.…”

Bounds on the solution of a Cauchy-type problem involving a weighted sequential fractional derivative

“…In a series of articles, [14,15,16], Glushak studied the uniform wellposedness of a Cauchy-type problem with two fractional derivatives and bounded operator. He also proposed a criterion for the uniform correctness of unbounded operator.…”