Nadia Benkhettou, Abdelkrim Salim, Jamal Eddine Lazreg, Mouffak Benchohra

A Study on Some New Conformable Fractional Differential Equations with Retardation and Anticipation

abstract:
In this paper, we present some results on the existence and uniqueness of the class of problems for nonlinear fractional differential equations with some new generalized conformable derivatives with retardation and anticipation. For our proofs, we employ some suitable fixed-point theorems. Finally, we provide two illustrative examples.

Mathematics Subject Classification: 26A33, 34A08, 34K37

Key words and phrases: Implicit differential equations, Riemann-Liouville fractional derivative, Caputo fractional derivative, fractional differential equations, improved conformable fractional derivative, existence, retardation, anticipation, fixed point