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

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

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Abstract

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In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type $\left({D}^{\alpha ₙ}-{\sum }_{i=1}^{n-1}{a}_{i}{D}^{{\alpha }_{i}}\right)x\left(t\right)\in F\left(t,x\left(\phi \left(t\right)\right)\right)$, a.e. on (0,1), ${I}^{1-\alpha ₙ}x\left(0\right)=c$, 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.

How to cite

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Hussein 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 -

References

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