Baleanu, DumitruAl-Refai, Mohammed2022-03-242025-09-182022-03-242025-09-182021Al-Refai, Mohammed; Baleanu, Dumitru (2021). "Comparison principles of fractional differential equations with non-local derivative and their applications", AIMS Mathematics, Vol. 6, No. 2, pp. 1443-1451.2473-6988https://doi.org/10.3934/math.2021088https://hdl.handle.net/20.500.12416/13147In this paper, we derive and prove a maximum principle for a linear fractional differential equation with non-local fractional derivative. The proof is based on an estimate of the non-local derivative of a function at its extreme points. A priori norm estimate and a uniqueness result are obtained for a linear fractional boundary value problem, as well as a uniqueness result for a nonlinear fractional boundary value problem. Several comparison principles are also obtained for linear and nonlinear equations.eninfo:eu-repo/semantics/openAccessFractional Differential EquationsMaximum PrincipleFractional DerivativesArticle10.3934/math.20210882-s2.0-85107751015