A Class of Implicit Fractional $\\psi$-Hilfer Langevin Equation with Time Delay and Impulse in the Weighted Space

Authors : Ayoub Louakar, Ahmed Kajounı, Khalid Hilal, Hamid Lmou

Pages : 88-103

Doi:10.33434/cams.1425019

View : 62 | Download : 70

Publication Date : 2024-06-30

Article Type : Research Paper

Abstract :In this paper, the Ulam-Hyers-Rassias stability is discussed and the existence and uniqueness of solutions for a class of implicit fractional $\\psi$-Hilfer Langevin equation with impulse and time delay are investigated. A novel form of generalized Gronwall inequality is introduced. Picard operator theory is employed in authour’s analysis. An example will be given to support the validity of our findings.
Keywords : Existence and uniqueness, Generalized Gronwall inequality, \\psi Hilfer Langevin equation, Picard operator theory, Ulam Hyers Rassias stability