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A study on certain properties of generalized M-special matrix functions and its applications.

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Τίτλος: A study on certain properties of generalized M-special matrix functions and its applications.
Συγγραφείς: Khan, Nabiullah1 (AUTHOR) nukhanmath@gmail.com, Sk, Rakibul1 (AUTHOR) rakibulsk375@gmail.com
Πηγή: Analysis (0174-4747). Aug2026, Vol. 46 Issue 3, p73-87. 15p.
Θεματικοί όροι: *Matrix functions, *Hypergeometric functions, *Derivatives (Mathematics), *Laplace transformation, *Fractional calculus, *Integrals
Περίληψη: The aim of this work is to introduce generalized M-gamma and M-beta matrix functions based on the generalized M-series with matrix arguments. By employing the beta function, we define several important classes of hypergeometric matrix functions, including the generalized M-Gauss, M-confluent, M-Appell, and M-Lauricella hypergeometric matrix functions. Various particular cases are examined to illustrate how these newly defined functions extend and unify several existing results in matrix analysis. Furthermore, we establish fundamental properties such as integral representations and derivative formulas. As an application, the Laplace transforms of the M-Gauss and M-confluent hypergeometric matrix functions are derived, and their significance in fractional calculus is explored. The proposed framework offers a powerful analytical tool for solving fractional differential equations and significantly broadens the scope of matrix-valued special function theory. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων: Academic Search Index
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An: 195835016
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  Data: A study on certain properties of generalized M-special matrix functions and its applications.
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  Data: <searchLink fieldCode="AR" term="%22Khan%2C+Nabiullah%22">Khan, Nabiullah</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> nukhanmath@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Sk%2C+Rakibul%22">Sk, Rakibul</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rakibulsk375@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Analysis+%280174-4747%29%22">Analysis (0174-4747)</searchLink>. Aug2026, Vol. 46 Issue 3, p73-87. 15p.
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  Data: *<searchLink fieldCode="DE" term="%22Matrix+functions%22">Matrix functions</searchLink><br />*<searchLink fieldCode="DE" term="%22Hypergeometric+functions%22">Hypergeometric functions</searchLink><br />*<searchLink fieldCode="DE" term="%22Derivatives+%28Mathematics%29%22">Derivatives (Mathematics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Laplace+transformation%22">Laplace transformation</searchLink><br />*<searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br />*<searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The aim of this work is to introduce generalized M-gamma and M-beta matrix functions based on the generalized M-series with matrix arguments. By employing the beta function, we define several important classes of hypergeometric matrix functions, including the generalized M-Gauss, M-confluent, M-Appell, and M-Lauricella hypergeometric matrix functions. Various particular cases are examined to illustrate how these newly defined functions extend and unify several existing results in matrix analysis. Furthermore, we establish fundamental properties such as integral representations and derivative formulas. As an application, the Laplace transforms of the M-Gauss and M-confluent hypergeometric matrix functions are derived, and their significance in fractional calculus is explored. The proposed framework offers a powerful analytical tool for solving fractional differential equations and significantly broadens the scope of matrix-valued special function theory. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1515/anly-2025-0007
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 73
    Subjects:
      – SubjectFull: Matrix functions
        Type: general
      – SubjectFull: Hypergeometric functions
        Type: general
      – SubjectFull: Derivatives (Mathematics)
        Type: general
      – SubjectFull: Laplace transformation
        Type: general
      – SubjectFull: Fractional calculus
        Type: general
      – SubjectFull: Integrals
        Type: general
    Titles:
      – TitleFull: A study on certain properties of generalized M-special matrix functions and its applications.
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            NameFull: Khan, Nabiullah
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          Name:
            NameFull: Sk, Rakibul
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          Dates:
            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 01744747
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            – Type: volume
              Value: 46
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              Value: 3
          Titles:
            – TitleFull: Analysis (0174-4747)
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