# Set-valued fractional order differential equations in the space of summable functions

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2008)

- Volume: 28, Issue: 1, page 83-93
- ISSN: 1509-9407

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topHussein A.H. Salem. "Set-valued fractional order differential equations in the space of summable functions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 28.1 (2008): 83-93. <http://eudml.org/doc/271184>.

@article{HusseinA2008,

abstract = {In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type
$(D^\{αₙ\} - ∑_\{i=1\}^\{n-1\} a_i D^\{α_i\})x(t) ∈ F(t,x(φ(t)))$,
a.e. on (0,1), $I^\{1 - αₙ\} x(0) = c$, αₙ ∈ (0,1),
where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.},

author = {Hussein A.H. Salem},

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

keywords = {fractional calculus; set-valued problem},

language = {eng},

number = {1},

pages = {83-93},

title = {Set-valued fractional order differential equations in the space of summable functions},

url = {http://eudml.org/doc/271184},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Hussein A.H. Salem

TI - Set-valued fractional order differential equations in the space of summable functions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2008

VL - 28

IS - 1

SP - 83

EP - 93

AB - In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type
$(D^{αₙ} - ∑_{i=1}^{n-1} a_i D^{α_i})x(t) ∈ F(t,x(φ(t)))$,
a.e. on (0,1), $I^{1 - αₙ} x(0) = c$, αₙ ∈ (0,1),
where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.

LA - eng

KW - fractional calculus; set-valued problem

UR - http://eudml.org/doc/271184

ER -

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