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<p>This paper investigates the existence of solutions to Jackson’s 2-dimensional quantum integral equations. First, we introduce a functional involving 2-dimensional <i>q</i>-integral equations modeled on the Banach algebra of continuous functions on the domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\([0,1] \times [0,1]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> <mo>×</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>. Next, we demonstrate the existence of solutions to these equations by using the concept of measure of noncompactness and Petryshyn’s fixed point theorem. Finally, we present a few suitable examples to illustrate our results. Finally, it is concluded that the existence theorem stated in this article can be a generalization of recent research publications in applied scientific fields.</p>

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Analysis of the solvability of 2-dimensional quantum fractional integral equation

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Hamid Reza Sahebi,
  • Manochehr Kazemi,
  • Mohammad Esmael Samei

摘要

This paper investigates the existence of solutions to Jackson’s 2-dimensional quantum integral equations. First, we introduce a functional involving 2-dimensional q-integral equations modeled on the Banach algebra of continuous functions on the domain \([0,1] \times [0,1]\) [ 0 , 1 ] × [ 0 , 1 ] . Next, we demonstrate the existence of solutions to these equations by using the concept of measure of noncompactness and Petryshyn’s fixed point theorem. Finally, we present a few suitable examples to illustrate our results. Finally, it is concluded that the existence theorem stated in this article can be a generalization of recent research publications in applied scientific fields.