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(p, k) Matrix Mittag‐Leffler and Pochhammer Functions With Applications to Fractional Differential Systems.

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Title: (p, k) Matrix Mittag‐Leffler and Pochhammer Functions With Applications to Fractional Differential Systems.
Authors: Al–Sheikh, Mohamed S.1 (AUTHOR) mohammedali.2459@azhar.edu.eg, Bakhet, Ahmed1,2 (AUTHOR), Mahmoud, Ahmed Adly1 (AUTHOR), Zahran, Ahmed M.1 (AUTHOR), Cortés, J.-C. (AUTHOR) jccortes@imm.upv.es
Source: Abstract & Applied Analysis. 6/19/2026, Vol. 2026, p1-10. 10p.
Subject Terms: *Fractional differential equations, *Matrix functions
Abstract: In this study, we introduce the two‐parameter Pochhammer matrix function. Notably, we establish the (p, k) Pochhammer matrix symbol as a key new construct for our generalizations. Furthermore, we construct gamma and beta matrix functions of two parameters and prove properties similar to their classical counterparts. Additionally, we define the (p, k) Mittag‐Leffler matrix function, exploring its fundamental properties, computation methods, and practical applications in solving systems of linear fractional differential equations. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
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  Data: (p, k) Matrix Mittag‐Leffler and Pochhammer Functions With Applications to Fractional Differential Systems.
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  Data: <searchLink fieldCode="AR" term="%22Al–Sheikh%2C+Mohamed+S%2E%22">Al–Sheikh, Mohamed S.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mohammedali.2459@azhar.edu.eg</i><br /><searchLink fieldCode="AR" term="%22Bakhet%2C+Ahmed%22">Bakhet, Ahmed</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mahmoud%2C+Ahmed+Adly%22">Mahmoud, Ahmed Adly</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zahran%2C+Ahmed+M%2E%22">Zahran, Ahmed M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Cortés%2C+J%2E-C%2E%22">Cortés, J.-C.</searchLink> (AUTHOR)<i> jccortes@imm.upv.es</i>
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  Data: <searchLink fieldCode="JN" term="%22Abstract+%26+Applied+Analysis%22">Abstract & Applied Analysis</searchLink>. 6/19/2026, Vol. 2026, p1-10. 10p.
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  Data: *<searchLink fieldCode="DE" term="%22Fractional+differential+equations%22">Fractional differential equations</searchLink><br />*<searchLink fieldCode="DE" term="%22Matrix+functions%22">Matrix functions</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: In this study, we introduce the two‐parameter Pochhammer matrix function. Notably, we establish the (p, k) Pochhammer matrix symbol as a key new construct for our generalizations. Furthermore, we construct gamma and beta matrix functions of two parameters and prove properties similar to their classical counterparts. Additionally, we define the (p, k) Mittag‐Leffler matrix function, exploring its fundamental properties, computation methods, and practical applications in solving systems of linear fractional differential equations. [ABSTRACT FROM AUTHOR]
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        Value: 10.1155/aaa/6468748
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      – Code: eng
        Text: English
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        PageCount: 10
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      – SubjectFull: Fractional differential equations
        Type: general
      – SubjectFull: Matrix functions
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      – TitleFull: (p, k) Matrix Mittag‐Leffler and Pochhammer Functions With Applications to Fractional Differential Systems.
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            NameFull: Al–Sheikh, Mohamed S.
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            NameFull: Bakhet, Ahmed
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            – D: 19
              M: 06
              Text: 6/19/2026
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              Y: 2026
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              Value: 2026
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