EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS

Ankita Chandola; Manish Kumar Mishra

EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS

Abstract

Fractional calculus in mathematics has various applications in engineering and science, inequality theory and is also used in solving various integral equations. In the past few years, fractional calculus operators that contains different special functions have been discussed by many researchers. In our paper, our objective is to discuss image formulas for different fractional integral and differential operators using the extended hypergeometric and extended confluent hypergeometric function involving Appell series and Lauricella function. Fractional calculus operators that has Appell function in the kernel and Saigo fractional operator are used in this paper. The results investigated in this manuscript are general, novel and are used to discuss various special cases and more fascinating results involving other special functions and fractional calculus operators. We have also discussed the application and future scope along with a brief comparison with the existing literature.

Keywords

Thanks

The authors would like to extend their gratitude to the reviewers for their valuable comments in improving this manuscript.

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Details

Primary Language

English

Subjects

Real and Complex Functions (Incl. Several Variables), Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Ankita Chandola This is me
0000-0002-0768-4332
India

Manish Kumar Mishra ^* This is me
0000-0001-7036-8714
India

Publication Date

February 3, 2026

Submission Date

December 30, 2024

Acceptance Date

April 28, 2025

Published in Issue

Year 2026 Volume: 16 Number: 2

IZ

https://izlik.org/JA27CR82BP

Cite

RIS / Bibtex

APA

Chandola, A., & Kumar Mishra, M. (2026). EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS. TWMS Journal of Applied and Engineering Mathematics, 16(2), 214-235. https://izlik.org/JA27CR82BP

AMA

1.Chandola A, Kumar Mishra M. EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS. JAEM. 2026;16(2):214-235. https://izlik.org/JA27CR82BP

Chicago

Chandola, Ankita, and Manish Kumar Mishra. 2026. “EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics 16 (2): 214-35. https://izlik.org/JA27CR82BP.

EndNote

Chandola A, Kumar Mishra M (February 1, 2026) EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS. TWMS Journal of Applied and Engineering Mathematics 16 2 214–235.

IEEE

[1]A. Chandola and M. Kumar Mishra, “EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS”, JAEM, vol. 16, no. 2, pp. 214–235, Feb. 2026, [Online]. Available: https://izlik.org/JA27CR82BP

ISNAD

Chandola, Ankita - Kumar Mishra, Manish. “EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics 16/2 (February 1, 2026): 214-235. https://izlik.org/JA27CR82BP.

JAMA

1.Chandola A, Kumar Mishra M. EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS. JAEM. 2026;16:214–235.

MLA

Chandola, Ankita, and Manish Kumar Mishra. “EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 2, Feb. 2026, pp. 214-35, https://izlik.org/JA27CR82BP.

Vancouver

1.Ankita Chandola, Manish Kumar Mishra. EXPLORING FRACTIONAL CALCULUS OPERATORS IN CONTEXT WITH EXTENDED HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTION: IMAGE FORMULAS AND APPLICATIONS. JAEM [Internet]. 2026 Feb. 1;16(2):214-35. Available from: https://izlik.org/JA27CR82BP