- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 3 Issue: 1
- Existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential...
Existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions
Authors : Abdelouaheb Ardjouni, Ahcene Djoudi
Pages : 46-52
Doi:10.31197/atnaa.501118
View : 10 | Download : 8
Publication Date : 2019-03-31
Article Type : Research
Abstract :In this paper, we use the contraction mapping principle to obtain the existence, interval of existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions. We also use the generalization of Gronwall's inequality to show the estimate of the solutions.Keywords : Implicit fractional differential equations, Nonlocal conditions, Caputo-Hadamard fractional derivatives, Fixed point theorems, Existence, Uniqueness