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On Existence of Solutions of <i>q</i>-Perturbed Quadratic Integral Equations
Department of Mathematics, Al Faisaliah Campus, Sciences Faculty, King Abdulaziz University, Jeddah, Saudi Arabia
- 1 Department of Mathematics, Al Faisaliah Campus, Sciences Faculty, King Abdulaziz University, Jeddah, Saudi Arabia
American Journal of Computational Mathematics·Volume 06 (2016)·Pages 166–176·Published 27 April 2016·DOI10.4236/ajcm.2016.62018
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Abstract
We investigate a <i>q</i>-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our <i>q</i>-integral equation has a solution in <i>C</i> [0, 1] which is monotonic on [0, 1]. The monotonicity measures of noncompactness due to Banaś and Olszowy and Darbo’s theorem are the main tools used in the proof of our main result.
Keywords<i>q</i>-FractionalIntegral EquationMonotonic SolutionsDarbo TheoremMonotonicity Measure of Noncompactness
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