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Solutions of sum-type singular fractional q-integro-differential equation with $m$-point boundary value using quantum calculus
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  • Ali Ahmadian,
  • Shahram Rezapour,
  • Soheil Salahshour,
  • Mohammad Esmael Samei
Ali Ahmadian
Mediterranean University of Reggio Calabria Department of Informatics Mathematics Electronics and Transport
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Shahram Rezapour
Azarbaijan Shahid Madani University
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Soheil Salahshour
Bahcesehir Universitesi
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Mohammad Esmael Samei
Bu Ali Sina University
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In this study, we investigate the sum-type singular nonlinear fractional q-integro-differential $m$-point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo $q$-derivative, Riemann-Liouville fractional $q$-integral and the means of a fixed point theorem on a real Banach space $(\mathcal{X}, \|.\|)$ which has a partially order by using a cone $P \subset \mathcal{X}$. The proofs are based on solving the operator equation $\mathcal{O}_1 x + \mathcal{O}_2 x = x $ such that the operator $\mathcal{O}_1$, $\mathcal{O}_2$ are $r$-convex, sub-homogeneous, respectively and define on cone $P$. As applications, we provide an example illustrating the primary effects.

Peer review status:ACCEPTED

20 Jan 2020Submitted to Mathematical Methods in the Applied Sciences
25 Jan 2020Submission Checks Completed
25 Jan 2020Assigned to Editor
25 Jan 2020Reviewer(s) Assigned
01 Feb 2020Review(s) Completed, Editorial Evaluation Pending
02 Feb 2020Editorial Decision: Revise Major
13 Feb 20201st Revision Received
13 Feb 2020Assigned to Editor
13 Feb 2020Submission Checks Completed
13 Feb 2020Reviewer(s) Assigned
15 Feb 2020Review(s) Completed, Editorial Evaluation Pending
12 Apr 2020Editorial Decision: Revise Major
21 May 20202nd Revision Received
22 May 2020Submission Checks Completed
22 May 2020Assigned to Editor
22 May 2020Reviewer(s) Assigned
24 May 2020Review(s) Completed, Editorial Evaluation Pending
25 May 2020Editorial Decision: Accept