The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses

Saïd Abbas; Mouffak Benchohra

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

  • Volume: 30, Issue: 1, page 141-161
  • ISSN: 1509-9407

Abstract

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In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.

How to cite

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Saïd Abbas, and Mouffak Benchohra. "The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.1 (2010): 141-161. <http://eudml.org/doc/271178>.

@article{SaïdAbbas2010,
abstract = {In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.},
author = {Saïd Abbas, Mouffak Benchohra},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {impulsive hyperbolic differential inclusion; fractional order; upper solution; lower solution; left-sided mixed Riemann-Liouville integral; Caputo fractional-order derivative; fixed point; Caputo fractional-order derivative, fixed point},
language = {eng},
number = {1},
pages = {141-161},
title = {The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses},
url = {http://eudml.org/doc/271178},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Saïd Abbas
AU - Mouffak Benchohra
TI - The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2010
VL - 30
IS - 1
SP - 141
EP - 161
AB - In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.
LA - eng
KW - impulsive hyperbolic differential inclusion; fractional order; upper solution; lower solution; left-sided mixed Riemann-Liouville integral; Caputo fractional-order derivative; fixed point; Caputo fractional-order derivative, fixed point
UR - http://eudml.org/doc/271178
ER -

References

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Citations in EuDML Documents

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  1. Saïd Abbas, Mouffak Benchohra, Lech Górniewicz, Fractional order impulsive partial hyperbolic differential inclusions with variable times
  2. Said Abbas, Mouffak Benchohra, A global uniqueness result for fractional order implicit differential equations
  3. Saïd Abbas, Eman Alaidarous, Wafaa Albarakati, Mouffak Benchohra, Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions
  4. Saïd Abbas, Mouffak Benchohra, Upper and Lower Solutions Method for Darboux Problem for Fractional Order Implicit Impulsive Partial Hyperbolic Differential Equations

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