SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT

doi:10.1016/S0252-9602(16)30125-4

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 195-204.doi: 10.1016/S0252-9602(16)30125-4

SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT

Juan J. NIETO^1,2, Bessem SAMET³

1. Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain;
2. Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
3. Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

收稿日期:2015-10-14 修回日期:2016-05-03 出版日期:2017-02-25 发布日期:2017-02-25
通讯作者: Bessem SAMET,E-mail:bsamet@ksu.edu.sa E-mail:bsamet@ksu.edu.sa
作者简介:Juan J. NIETO,E-mail:juanjose.nieto.roig@usc.es
基金资助:
The first author acknowledges partial financial support by the Ministerio de Economica y Competitividad of Spain under grant MTM2013-43014-P, XUNTA under grants R2014/002 and GRC2015/004, and co-financed by the European Community fund FEDER. The second author extends his appreciation to Distinguished Scientist Fellowship Program (DSFP) at King Saud University (Saudi Arabia).

SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT

Juan J. NIETO^1,2, Bessem SAMET³

1. Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain;
2. Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
3. Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Received:2015-10-14 Revised:2016-05-03 Online:2017-02-25 Published:2017-02-25
Contact: Bessem SAMET,E-mail:bsamet@ksu.edu.sa E-mail:bsamet@ksu.edu.sa
About author:Juan J. NIETO,E-mail:juanjose.nieto.roig@usc.es
Supported by:
The first author acknowledges partial financial support by the Ministerio de Economica y Competitividad of Spain under grant MTM2013-43014-P, XUNTA under grants R2014/002 and GRC2015/004, and co-financed by the European Community fund FEDER. The second author extends his appreciation to Distinguished Scientist Fellowship Program (DSFP) at King Saud University (Saudi Arabia).

摘要/Abstract

摘要：

In this paper, we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function, which generalizes the Riemann-Liouville fractional integral and the Hadamard fractional integral. We establish an existence result to such kind of equations using a generalized version of Darbo's theorem associated to a certain measure of noncompactness. Some examples are presented.

关键词: umplicit fractional integral equation, measure of noncompactness, Darbo's theorem

Abstract:

Key words: umplicit fractional integral equation, measure of noncompactness, Darbo's theorem

Juan J. NIETO, Bessem SAMET. SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT[J]. 数学物理学报(英文版), 2017, 37(1): 195-204.

Juan J. NIETO, Bessem SAMET. SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT[J]. Acta mathematica scientia,Series B, 2017, 37(1): 195-204.

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SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT

SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT

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