Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 98, pp. 122.
Nonlinear fractional differential equations and inclusions
of arbitrary order and multistrip boundary conditions
Bashir Ahmad, Sotiris K. Ntouyas
Abstract:
We study boundary value problems of nonlinear fractional
differential equations and inclusions of order
,
with multistrip boundary conditions. Multistrip boundary
conditions may be regarded as the generalization of multipoint
boundary conditions. Our problem is new in the sense
that we consider a nonlocal strip condition of the form:
which can be viewed as an extension of a multipoint nonlocal
boundary condition:
In fact, the strip condition corresponds to a continuous distribution
of the values of the unknown function on arbitrary finite
segments
of the interval
and the effect
of these strips is accumulated at
.
Such problems occur in
the applied fields such as wave propagation and geophysics. Some
new existence and uniqueness results are obtained by using a
variety of fixed point theorems. Some illustrative examples are
also discussed.
Submitted May 20, 2012. Published June 12, 2012.
Math Subject Classifications: 26A33, 34A60, 34B10, 34B15.
Key Words: Fractional differential inclusions; integral boundary conditions;
existence; contraction principle; Krasnoselskii's fixed point theorem;
LeraySchauder degree; LeraySchauder nonlinear alternative;
nonlinear contractions.
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Bashir Ahmad
Department of Mathematics, Faculty of Science
King Abdulaziz University
P.O. Box 80203, Jeddah 21589, Saudi Arabia
email: bashir_qau@yahoo.com


Sotiris K. Ntouyas
Department of Mathematics
University of Ioannina
451 10 Ioannina, Greece
email: sntouyas@uoi.gr

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