Explicit evaluations of subfamilies of the hypergeometric function 3F2(1) along with specific fractional integrals

被引：0

作者：

Zaidi, Abdelhamid ^{[1
]}

Almuthaybiri, Saleh ^{[1
]}

机构：

[1] Qassim Univ, Coll Sci, Dept Math, POB 6644, Buraydah 51452, Saudi Arabia

来源：

AIMS MATHEMATICS | 2025年 / 10卷 / 03期

关键词：

fractional integrals; fractional derivatives; Gauss hypergeometric functions; generalized hypergeometric functions; numerical series; power series; decomposition into partial fractions; differential equations;

D O I：

10.3934/math.2025264

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present study explores the application of hypergeometric functions in evaluating fractional integrals, providing a comprehensive framework to bridge fractional calculus and special functions. As a generalization of classical integrals, fractional integrals have gained prominence due to their wide applicability in modeling anomalous diffusion, viscoelastic systems, and other non-local phenomena. Hypergeometric functions, renowned for their rich analytical properties and ability to represent solutions to differential equations, offer an elegant and versatile tool for solving fractional integrals. In this paper, we evaluate a new class of fractional integrals, presenting results that contribute significantly to the study of generalized hypergeometric functions, particularly 3F2(1). The results reveal previously unexplored connections within these functions, providing new insights and extending their applicability. Furthermore, evaluating these fractional integrals holds promise for advancing the theoretical understanding and practical applications of fractional differential equations.

引用

页码：5731 / 5761

页数：31

共 31 条

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