General fractional differential equations of order $$\alpha \in (1,2)$$ α ∈ ( 1 , 2 ) and Type $$\beta \in [0,1]$$ β ∈ [ 0 , 1 ] in Banach spaces

Existence results for nonlinear fractional differential equations with integral initial value conditions involving Hilfer fractional derivatives

“…Meanwhile, inspired by questions mentioned in [13][14][15][16][17][18][19][20] and references therein, we will discuss existence results by means of Schaefer's fixed point theorem [21,22] to explore the existence results for the nonlinear differential equation (1.1) in relation to Hilfer fractional derivative. This paper is organized as follows, In Section 2, as preliminaries, the fundamental definitions and properties are given.…”

Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions

“…The fractional differential equations with Hilfer (generalized Riemann-Liouville) fractional derivative have recently attracted the attention of some authors interested in fractional calculus (see [1,2,9,16,20,21,25,26]). On the other hand, autonomous and non-autonomous systems of Hilfer fractional differential inclusions and equations play a considerable role that can not be over looked in the recent published researches.…”

Existence and uniqueness for a kind of nonlocal fractional evolution equations on the unbounded interval

“…To the best of our knowledge, fractional evolution equations have attracted more and more attention recently [18][19][20][21][22][23][24][25][26][27][28]. For instance, in [20], Zhou investigated a class of nonlocal evolution equations of fractional order…”