Existence of positive solution of a singular partial differential equation

Shu Qin Zhang

Mathematica Bohemica (2008)

• Volume: 133, Issue: 1, page 29-40
• ISSN: 0862-7959

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Abstract

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Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.

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Zhang, Shu Qin. "Existence of positive solution of a singular partial differential equation." Mathematica Bohemica 133.1 (2008): 29-40. <http://eudml.org/doc/250525>.

@article{Zhang2008,
abstract = {Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.},
author = {Zhang, Shu Qin},
journal = {Mathematica Bohemica},
keywords = {mixed Riemann-Liouville fractional derivative; function space concerning fractional derivative; existence and uniqueness; positive solution; fixed point theorem; mixed Riemann-Liouville fractional derivative; function space concerning fractional derivative; existence and uniqueness; positive solution; fixed point theorem},
language = {eng},
number = {1},
pages = {29-40},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of positive solution of a singular partial differential equation},
url = {http://eudml.org/doc/250525},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Zhang, Shu Qin
TI - Existence of positive solution of a singular partial differential equation
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 1
SP - 29
EP - 40
AB - Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.
LA - eng
KW - mixed Riemann-Liouville fractional derivative; function space concerning fractional derivative; existence and uniqueness; positive solution; fixed point theorem; mixed Riemann-Liouville fractional derivative; function space concerning fractional derivative; existence and uniqueness; positive solution; fixed point theorem
UR - http://eudml.org/doc/250525
ER -

References

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1. Integrals and Derivatives of Fractional Order and Their Applications, Tekhnika, Minsk, 1987. (Russian) (1987) MR0915556
2. 10.1016/S0960-0779(02)00586-6, Chaos, Solitons, Fractals 18 (2003), 135–140. (2003) MR1984554DOI10.1016/S0960-0779(02)00586-6
3. A Cauchy problem for evolution equations of fractional order, Differential Equations 25 (1989), 967–974. (1989) MR1014153
4. 10.1023/B:DIEQ.0000011289.79263.02, Differential Equations 39, 8 (2003), 1150–1158. (2003) MR2198241DOI10.1023/B:DIEQ.0000011289.79263.02
5. 10.1007/s11072-005-0015-9, Nonlinear Oscillations 7 (2004 2004), 318–325. (2004 2004) MR2151816DOI10.1007/s11072-005-0015-9
6. Fractional calculus and function spaces, Journal of Fractional Calculus 6 (1994), 45–53. (1994) MR1301228

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