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Uniqueness of Solutions, Stability and Simulations for a Differential Problem Involving Convergent Series and Time Variable Singularities
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  • Yazid GOUARI,
  • Zoubir Dahmani,
  • Meriem Mansouria BELHAMITI,
  • Mehmet Zeki Sarikaya
Ecole Normale Superieure
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Zoubir Dahmani
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Meriem Mansouria BELHAMITI
Université Abdelhamid Ibn Badis de Mostaganem
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Mehmet Zeki Sarikaya
Duzce Universitesi
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We focus on a new type of nonlinear integro-differential equations with nonlocal integral conditions. The considered problem has one nonlinearity with time variable singularity. It involves also some convergent series combined to Riemann-Liouville integrals. We prove a uniqueness of solutions for the proposed problem, then, we provide some examples to illustrate this result. Also, we discuss the Ulam-Hyers stability for the problem. Some numerical simulations, using Rung Kutta method, are discussed too. At the end, a conclusion follows.

Peer review status:UNDER REVIEW

04 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
06 Nov 2021Assigned to Editor
06 Nov 2021Submission Checks Completed
12 Nov 2021Reviewer(s) Assigned