“…Some recent works on fractional differential equations involving Riemann Liouville and Caputo-type fractional derivatives are studied using nonlinear analysis methods such as Krasnoselskii fixed-point Theorems (Agarwal and O'Regan, 1998;Ghanmi and Horrigue, 2018;Guo et al, 2007;Guo et al, 2008), Leray-Schauder alternative (Ghanmi and Horrigue, 2019;Qi et al, 2017), sub-solution and super-solution methods (Wang et al, 2019;Mâagli et al, 2015) and iterative techniques (Liu et al, 2013). Hadamard (1892) introduced an important fractional derivative, which differs from the above-mentioned ones because its definition involves logarithmic function of arbitrary exponent and named as Hadamard derivative.…”