Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 140
Existence and uniqueness results for Hilfer Langevin fractional pantograph differential equation and inclusion
Hamid Lmou, Khalid Hilal, Ahmed Kajouni
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 19, 2022
March 03, 2128
April 15, 2128

Abstract: This paper discuss the existence and uniqueness of solution for Hilfer Langevin fractional pantograph differential equation and inclusion, which are a special class of delay differential equations. The novelty of this work is that it is more general than the works based on the derivative of Caputo and Riemann-Liouville, because when $\beta =0$ we get the Riemann-Liouville fractional derivative and when $\beta=1$ we get the Caputo fractional derivative. In the first, we give some definitions, theorems, lemmas that are used through this manuscript. secondly, we give our existence results, ...