EXTENDED HYPERGEOMETRIC LOGARITHMIC FUNCTIONS AND ITS APPLICATION IN GENERALIZED FRACTIONAL KINETIC EQUATIONS

Mohamed Abdalla, Yahya Almalki, Ibrahim Mekawy () and Hala Abd-Elmageed
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Mohamed Abdalla: Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
Yahya Almalki: Mathematics Department, Faculty of Science, King Khalid University, Abha, Saudi Arabia
Ibrahim Mekawy: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
Hala Abd-Elmageed: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia1Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-9

Abstract: An extension of the beta function that introduces the logarithmic mean is utilized here to extend hypergeometric functions such as Gauss and Kummer hypergeometric logarithmic functions. These functions encompass various well-known special functions as specific cases. This expansion is expected to be beneficial. The text explains some characteristics of the Gauss and Kummer hypergeometric logarithmic functions. Furthermore, it explores the solution of a generalized fractional kinetic equation using these newly extended functions.

Keywords: Hypergeometric Logarithmic Functions; Integral Representations; Fractional Kinetic Equation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400948

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