Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions

Bashir Ahmad; Sotiris Ntouyas

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 3, page 451-465
  • ISSN: 0862-7959

Abstract

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In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the multivalued map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative of Leray-Schauder type for single-valued maps with a selection theorem due to Bressan and Colombo, while in the third case we use a fixed point theorem for multivalued contractions due to Covitz and Nadler.

How to cite

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Ahmad, Bashir, and Ntouyas, Sotiris. "Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions." Mathematica Bohemica 139.3 (2014): 451-465. <http://eudml.org/doc/262040>.

@article{Ahmad2014,
abstract = {In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the multivalued map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative of Leray-Schauder type for single-valued maps with a selection theorem due to Bressan and Colombo, while in the third case we use a fixed point theorem for multivalued contractions due to Covitz and Nadler.},
author = {Ahmad, Bashir, Ntouyas, Sotiris},
journal = {Mathematica Bohemica},
keywords = {differential inclusion; nonlocal condition; integral boundary condition; Leray Schauder alternative; fixed point theorem; differential inclusion; topological methods; nonlocal conditions; integral boundary conditions; Leray-Schauder alternative; fixed point theorem},
language = {eng},
number = {3},
pages = {451-465},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions},
url = {http://eudml.org/doc/262040},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Ahmad, Bashir
AU - Ntouyas, Sotiris
TI - Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 3
SP - 451
EP - 465
AB - In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the multivalued map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative of Leray-Schauder type for single-valued maps with a selection theorem due to Bressan and Colombo, while in the third case we use a fixed point theorem for multivalued contractions due to Covitz and Nadler.
LA - eng
KW - differential inclusion; nonlocal condition; integral boundary condition; Leray Schauder alternative; fixed point theorem; differential inclusion; topological methods; nonlocal conditions; integral boundary conditions; Leray-Schauder alternative; fixed point theorem
UR - http://eudml.org/doc/262040
ER -

References

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