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<p>We present a formal study of a particular class of fractional operators, namely the generalised Erdélyi–Kober fractional calculus operators. Emphasising the role of transmutation relations with the classical Erdélyi–Kober operator, we use these connections to establish several fundamental properties of the generalised operators. We also derive the limit and mapping properties between functional spaces, along with proving their boundedness in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> spaces. Furthermore, we develop the operational calculus for the generalised Erdélyi–Kober operator, including the construction of a projector operator and the application of the Mellin transform. A condition for the existence of the Mellin transform of these operators is also provided.</p>

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On the generalised Erdélyi–Kober fractional operators

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Amna Tanveer,
  • Hafiz Muhammad Fahad,
  • Mujeeb ur Rehman

摘要

We present a formal study of a particular class of fractional operators, namely the generalised Erdélyi–Kober fractional calculus operators. Emphasising the role of transmutation relations with the classical Erdélyi–Kober operator, we use these connections to establish several fundamental properties of the generalised operators. We also derive the limit and mapping properties between functional spaces, along with proving their boundedness in \(L_p\) L p spaces. Furthermore, we develop the operational calculus for the generalised Erdélyi–Kober operator, including the construction of a projector operator and the application of the Mellin transform. A condition for the existence of the Mellin transform of these operators is also provided.