TY - JOUR T1 - Existence of Solution for a Nonlinear Fractional Order Differential Equation with a Quadratic Perturbations AU - Chefnaj, Najat AU - Kajounı, Ahmed AU - Hilal, Khalid PY - 2022 DA - September DO - 10.53006/rna.1124961 JF - Results in Nonlinear Analysis JO - RNA PB - Erdal KARAPINAR WT - DergiPark SN - 2636-7556 SP - 360 EP - 371 VL - 5 IS - 3 LA - en AB - In this work, we prove the existence of a solution for the initial value problem of nonlinear fractional differential equation with quadratic perturbations involving the Caputo fractional derivative (cDα0+−ρtcDβ0+)(x(t)f(t,x(t)))=g(t,x(t)),t∈J=[0,1],1<α<2,0<β<α(cD0+α−ρtcD0+β)(x(t)f(t,x(t)))=g(t,x(t)),t∈J=[0,1],1<α<2,0<β<αwith conditions x0=x(0)f(0,x(0))x0=x(0)f(0,x(0)) and \\x1=x(1)f(1,x(1))x1=x(1)f(1,x(1)). Dhage's fixed-pointthe theorem was used to establish this existence. As an application, we have givenexample to demonstrate the effectiveness of our main result. 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