Document Type : Research Article
Authors
1
Laboratory‎, ‎FIMA‎, ‎UDBKM‎, ‎Khemis Miliana University‎, ‎Algeria
2
Department of Mathematics‎, ‎Faculty of Science‎, ‎Bu-Ali Sina University‎, ‎Hamedan‎, ‎Iran
3
Gofa Camp, Near Gofa Industrial College and German Adebabay, Nifas Silk-Lafto, 26649 Addis Ababa, Ethiopia; Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia
4
Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran
10.22128/ansne.2026.3155.1180
Abstract
In this manuscript, we investigate the nonlinear singular $q-$differential equation of Lane-Emden type, by using the general Riemann-Liouville integral and Caputo derivative of $q-$fractional order operators. First, our approach to prove existence and uniqueness is Banach's contraction principle. Then, in the next step, to confirm the existence of at least one solution, we take help from fixed point theorem of Schaefer. Moreover, the stabilities in the sense of Ulam-Hyers and Ulam-Hyers-Rassias are also defined and examined. Finally, we present a comprehensive example to show the applicability of the outcomes.
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