Application of Fractional Quantum Calculus on Lane-Emden Type Problem Involving Two Fractional q_Derivatives

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

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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Analytical and Numerical Solutions for Nonlinear Equations
Volume 11, Issue 1
June 2026
Pages 32-50

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History

  • Receive Date: 17 November 2025
  • Revise Date: 17 February 2026
  • Accept Date: 15 March 2026
  • Publish Date: 07 June 2026

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