Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 11 1 2026 06 07 Application of Fractional Quantum Calculus on Lane-Emden Type Problem Involving Two Fractional q_Derivatives 32 50 2090 10.22128/ansne.2026.3155.1180 EN Mohamed Houas Laboratory‎, ‎FIMA‎, ‎UDBKM‎, ‎Khemis Miliana University‎, ‎Algeria 0000-0001-6256-0511 ‎Mohammad Esmael Samei Department of Mathematics‎, ‎Faculty of Science‎, ‎Bu-Ali Sina University‎, ‎Hamedan‎, ‎Iran 0000-0002-5450-3127 Mohammed K. A. ‎Kaabar 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 0000-0002-5450-3127 Manochehr Kazemi Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran 0000-0001-8392-6690 Journal Article 2025 11 17 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. https://ansne.du.ac.ir/article_2090_a2e8588b0c3d56c7a45b7e2e7a036536.pdf