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

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

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (1): 195-204.doi: 10.1016/S0252-9602(16)30125-4

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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).

Abstract

Abstract:

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.

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].Acta mathematica scientia,Series B, 2017, 37(1): 195-204.

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References

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

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