Langevin differential equation of fractional order in non compactness Banach space

Solvability for a nonlinear differential problem of Langevin type via phi-Caputo approach

“…The fractional calculus has a significant role in various scientific fields, see for instance [10,16,17]. As applied results of this significant role, we shed light on the fact that fractional order differential equations have attired attention of many researchers that have worked in different fields of research [7,8,15]. However, most of these research works have been achieved by means of fractional derivatives of type: RiemannLiouville, Hadamard, Katugampola, Grunwald Letnikov and Caputo.…”

Solvability for a Differential Systems via Phi-Caputo Approach

“…In most of the present articles, Schauder, Krasnoselskii, Darbo, or M nch theories have been used to prove existence of solutions of nonlinear fractional differential equations with some restrictive conditions [9][10][11].…”

A new tripled system of hybrid differential equations with φ-Caputo derivatives

“…In most of these published articles, Schauder, Krasnoselskii, Darbo, or Monch theories have been used to prove existence of solutions of nonlinear fractional equations. See also [16][17][18][19][20][21] for other results on such problems. In particular, some authors have recently worked on the solutions for hybrid fractional problems [22][23], this is in one hand.…”