Solvability of some fractional-order three point boundary value problems
Authors :
A. M. A. El-Sayed 1 * and Abd El-Salam Sh. A. 2
Author Address :
1 Faculty of Science, Alexandria University, Alexandria, Egypt.
2 Faculty of Science, Damanhour University, Egypt.
*Corresponding author.
Abstract :
In this work, we prove the existence of at least one solution of the two fractional-order three point boundary
value problems:
[
left{egin{array}{c}D^eta~u(t)~+~lambda~a(t)~f(u(t))~=~0,~eta~in~(1,2],~t~in~(0,1),\
u(0)~=~0,~alpha~u(eta)~=~u(1),~0~<~eta~<1,
~0~leq~alpha~eta~<~1.end{array}
ight.
]
and
[
left{egin{array}{c}D^eta~u(t)~+~lambda~a(t)~f(u(t))~=~0,~eta~in~(1,2],~t~in~(0,1),\
u’(0)~=~0,~alpha~u’(eta)~=~u(1),~0~<~eta~<1,
~0~leq~alpha~eta~<~1.end{array}
ight.
].
Keywords :
Fractional calculus; Three point boundary value problems.
DOI :
Article Info :
Received : September 06, 2017; Accepted : January 11, 2018.
