Article citationsMore>>

Abdeljawad, T. and Baleanu, D. (2011) Caputo q-Fractional Initial Value Problems and a q-Analogue Mittag-Leffler Function. Communications in Nonlinear Science and Numerical Simulation, 16, 4682-4688.
http://dx.doi.org/10.1016/j.cnsns.2011.01.026

has been cited by the following article:

• TITLE: On Existence of Solutions of q-Perturbed Quadratic Integral Equations

  AUTHORS: Maryam Al-Yami

  KEYWORDS: q-Fractional, Integral Equation, Monotonic Solutions, Darbo Theorem, Monotonicity Measure of Noncompactness

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.6 No.2, June 29, 2016

  ABSTRACT: We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C [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.