Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space

Mouffak Benchohra; Soufyane Bouriah; Jamal E. Lazreg; Juan J. Nieto

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 1, page 15-26
  • ISSN: 0231-9721

Abstract

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In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.

How to cite

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Benchohra, Mouffak, et al. "Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.1 (2016): 15-26. <http://eudml.org/doc/286701>.

@article{Benchohra2016,
abstract = {In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.},
author = {Benchohra, Mouffak, Bouriah, Soufyane, Lazreg, Jamal E., Nieto, Juan J.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Hadamard’s fractional derivative; implicit fractional differential equations in Banach space; fractional integral; existence; Gronwall’s lemma for singular kernels; Measure of noncompactness; fixed point},
language = {eng},
number = {1},
pages = {15-26},
publisher = {Palacký University Olomouc},
title = {Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space},
url = {http://eudml.org/doc/286701},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Benchohra, Mouffak
AU - Bouriah, Soufyane
AU - Lazreg, Jamal E.
AU - Nieto, Juan J.
TI - Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 1
SP - 15
EP - 26
AB - In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.
LA - eng
KW - Hadamard’s fractional derivative; implicit fractional differential equations in Banach space; fractional integral; existence; Gronwall’s lemma for singular kernels; Measure of noncompactness; fixed point
UR - http://eudml.org/doc/286701
ER -

References

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