A global uniqueness result for fractional order implicit differential equations

Said Abbas; Mouffak Benchohra

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 4, page 605-614
  • ISSN: 0010-2628

Abstract

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In this paper we investigate the global existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of implicit hyperbolic fractional order differential equations by using a nonlinear alternative of Leray-Schauder type for contraction maps on Fréchet spaces.

How to cite

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Abbas, Said, and Benchohra, Mouffak. "A global uniqueness result for fractional order implicit differential equations." Commentationes Mathematicae Universitatis Carolinae 53.4 (2012): 605-614. <http://eudml.org/doc/252515>.

@article{Abbas2012,
abstract = {In this paper we investigate the global existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of implicit hyperbolic fractional order differential equations by using a nonlinear alternative of Leray-Schauder type for contraction maps on Fréchet spaces.},
author = {Abbas, Said, Benchohra, Mouffak},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {partial hyperbolic differential equation; fractional order; left-sided mixed Riemann-Liouville integral; mixed regularized derivative; solution; Fréchet space; fixed point; fractional differential equation of fractional order; Fréchet space; fixed point problem},
language = {eng},
number = {4},
pages = {605-614},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A global uniqueness result for fractional order implicit differential equations},
url = {http://eudml.org/doc/252515},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Abbas, Said
AU - Benchohra, Mouffak
TI - A global uniqueness result for fractional order implicit differential equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 4
SP - 605
EP - 614
AB - In this paper we investigate the global existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of implicit hyperbolic fractional order differential equations by using a nonlinear alternative of Leray-Schauder type for contraction maps on Fréchet spaces.
LA - eng
KW - partial hyperbolic differential equation; fractional order; left-sided mixed Riemann-Liouville integral; mixed regularized derivative; solution; Fréchet space; fixed point; fractional differential equation of fractional order; Fréchet space; fixed point problem
UR - http://eudml.org/doc/252515
ER -

References

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  2. Abbas S., Benchohra M., Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative, Commun. Math. Anal. 7 (2009), 62–72. Zbl1178.35371MR2535015
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  4. Abbas S., Benchohra M., Gorniewicz L., Existence theory for impulsive partial hyperbolic functional differential equations involving the Caputo fractional derivative, Sci. Math. Jpn. 72 (2010), 49–60. Zbl1200.26004MR2666846
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  8. Benchohra M., Graef J.R., Hamani S., 10.1080/00036810802307579, Appl. Anal. 87 (2008), no. 7, 851–863. MR2458962DOI10.1080/00036810802307579
  9. Benchohra M., Hamani S., Ntouyas S.K., Boundary value problems for differential equations with fractional order, Surv. Math. Appl. 3 (2008), 1–12. Zbl1198.26007MR2390179
  10. Benchohra M., Henderson J., Ntouyas S.K., Ouahab A., 10.1016/j.jmaa.2007.06.021, J. Math. Anal. Appl. 338 (2008), 1340–1350. MR2386501DOI10.1016/j.jmaa.2007.06.021
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