Solvability of some fractional-order three point boundary value problems

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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 :

10.26637/MJM0602/0015

Article Info :

Received : September 06, 2017; Accepted : January 11, 2018.

 

 

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