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<p>This study investigates a class of fractional integral equations involving Hadamard fractional integral operator. By virtue of Petryshyn’s fixed point theorem and the measure of non-compactness, we establish existence results for solutions within the Banach algebra <i>C</i>[1,&#xa0;<i>a</i>],&#xa0;<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(a&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>a</mi> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Notably, we do not impose the bounded requirement, commonly known as the “Sublinear condition”, as seen in existing literature. Through theoretical analysis, we demonstrate the existence of solutions for the considered class of Hadamard-type fractional integral equations. Furthermore, we investigate the uniqueness of solutions under certain restrictive conditions. Additionally, we provide some illustrative examples to illustrate the accuracy and applicability of our results. Finally, conclusions and future scopes are also presented. </p>

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Solvability for a Class of Hadamard-Type Fractional Integral Equation in a Banach Algebra

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • Sukanta Halder,
  • Deepmala

摘要

This study investigates a class of fractional integral equations involving Hadamard fractional integral operator. By virtue of Petryshyn’s fixed point theorem and the measure of non-compactness, we establish existence results for solutions within the Banach algebra C[1, a],  \(a>1\) a > 1 . Notably, we do not impose the bounded requirement, commonly known as the “Sublinear condition”, as seen in existing literature. Through theoretical analysis, we demonstrate the existence of solutions for the considered class of Hadamard-type fractional integral equations. Furthermore, we investigate the uniqueness of solutions under certain restrictive conditions. Additionally, we provide some illustrative examples to illustrate the accuracy and applicability of our results. Finally, conclusions and future scopes are also presented.