Acta mathematica scientia, Series B >
SOLVABILITY OF AN IMPLICIT FRACTIONAL INTEGRAL EQUATION VIA A MEASURE OF NONCOMPACTNESS ARGUMENT
Received date: 2015-10-14
Revised date: 2016-05-03
Online published: 2017-02-25
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).
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.
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 . DOI: 10.1016/S0252-9602(16)30125-4
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