Open AccessOn a Hadamard fractional boundary value problem for 3 < α ≤ 4.
Author(s) -
Haifa Bin Jebreen,
Lakhdar Ragoub
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1593/1/012007
Subject(s) - hadamard transform , mathematics , boundary value problem , hadamard three lines theorem , order (exchange) , function (biology) , fractional calculus , operator (biology) , mathematical analysis , value (mathematics) , class (philosophy) , pure mathematics , hadamard matrix , computer science , biochemistry , chemistry , finance , repressor , evolutionary biology , artificial intelligence , gene , transcription factor , economics , biology , statistics
This note deals with Hadamard fractional differential equation of order 3 < α ≤ 4, subject to a mixed boundary conditions on [1, e]. The investigation made here involves Hadamard integral operator of a function with a construction of an appropriate Green’s function. Using its properties as well as its maximum value, we will be able to get Hartman-Winter and Lyapunov-type inequalities for a class of Hadamard fractional differential equations. Finally, we will illustrate this result by giving an example.