Fractional Calculus involving (p, q)-Mathieu Type Series

• Published in: Applied mathematics and nonlinear sciences Vol. 5; no. 2; pp. 15 - 34
• Main Authors: Kaur, Daljeet, Agarwal, Praveen, Rakshit, Madhuchanda, Chand, Mehar
• Format: Journal Article
• Language: English
• Published: Beirut Sciendo 01.07.2020; De Gruyter Poland
• Subjects: Extended generalized Mathieu series; Fractional derivative operators; Fractional integral operators; Integral transforms
• ISSN: 2444-8656; 2444-8656
• DOI: 10.2478/amns.2020.2.00011

Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized ( , )-Mathieu type series. Then, their composition formulas by using the integral transforms are introduced. Further, a new generalized form of the fractional kinetic equation involving the series is also developed. The solutions of fractional kinetic equations are presented in terms of the Mittag-Leffler function. The results established here are quite general in nature and capable of yielding both known and new results.