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<p>In this work, we investigate higher-order Hilfer fractional Volterra-Fredholm integrodifferential (HOHFVFI) equations of order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(1&lt;\varrho &lt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>ϱ</mi> <mo>&lt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> and type <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\delta \in [0,1]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>δ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation> with infinite delay. We establish the existence of mild solutions in the presence of infinite delay by using the cosine family and the Laplace transform representations together with a measure of noncompactness and a fixed point argument. Then, we derive exact controllability results for the considered HOHFVFI system with infinite delay. To clarify the proposed structure, we provide an illustrative example to demonstrate the applicability of the theoretical findings.</p>

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Exact controllability for nonlinear Hilfer fractional Volterra-Fredholm integrodifferential equations \((1< \varrho < 2)\) with infinite delay based on the measure of noncompactness

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  • 发表日期：

    2026年4月22日

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  • Marimuthu Mohan Raja,
  • Kalyana Chakravarthy Veluvolu

摘要

In this work, we investigate higher-order Hilfer fractional Volterra-Fredholm integrodifferential (HOHFVFI) equations of order \(1<\varrho <2\) 1 < ϱ < 2 and type \(\delta \in [0,1]\) δ ∈ [ 0 , 1 ] with infinite delay. We establish the existence of mild solutions in the presence of infinite delay by using the cosine family and the Laplace transform representations together with a measure of noncompactness and a fixed point argument. Then, we derive exact controllability results for the considered HOHFVFI system with infinite delay. To clarify the proposed structure, we provide an illustrative example to demonstrate the applicability of the theoretical findings.