# Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

Saïd Abbas; Mouffak Benchohra; Mohamed Abdalla Darwish

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2016)

- Volume: 36, Issue: 2, page 155-179
- ISSN: 1509-9407

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topSaïd Abbas, Mouffak Benchohra, and Mohamed Abdalla Darwish. "Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 36.2 (2016): 155-179. <http://eudml.org/doc/289596>.

@article{SaïdAbbas2016,

abstract = {In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions},

author = {Saïd Abbas, Mouffak Benchohra, Mohamed Abdalla Darwish},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {fractional differential inclusion; left-sided mixed Riemann-Liouville integral; Caputo fractional order derivative; upper solution; lower solution; extremal solution; fixed point; Banach algebras; not instantaneous impulses},

language = {eng},

number = {2},

pages = {155-179},

title = {Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses},

url = {http://eudml.org/doc/289596},

volume = {36},

year = {2016},

}

TY - JOUR

AU - Saïd Abbas

AU - Mouffak Benchohra

AU - Mohamed Abdalla Darwish

TI - Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2016

VL - 36

IS - 2

SP - 155

EP - 179

AB - In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions

LA - eng

KW - fractional differential inclusion; left-sided mixed Riemann-Liouville integral; Caputo fractional order derivative; upper solution; lower solution; extremal solution; fixed point; Banach algebras; not instantaneous impulses

UR - http://eudml.org/doc/289596

ER -

## References

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