Abstract
In this study, we are concerned with the existence and uniqueness of solution for some nonlinear Hadamard fractional differential equations. Our results are based on different classical fixed point theorems. Some useful examples are presented in order to illustrate the validity of our main results.
Highlights
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
Some researches have extensively interested in the study of the fractional differential equations with p-Laplacian operators see for examples (Chamekh et al, 2018; Ding et al, 2015)
The main results of this study are summarized in the following theorems
Summary
Fractional differential equations have been acquired much attention due to its applications in a number of fields such as physics, mechanics, chemistry, biology, signal and image processing, see for example the books (Baleanu et al, 2012; Kilbas et al, 2006; Lakshmikantham et al, 2009; Yang et al, 2015).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. A very few authors established results along with p-Laplacian operator, us example in (Wang and Wang, 2016), the authors considered the following nonlinear Hadamard fractional differential problem: ( ) D p (D u (t )) = f (t,u (t )), t (1,T ), By using the Schauder fixed point Theorem, the existence of solutions is obtained.
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