<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized (<italic>p</italic>, <italic>q</italic>)-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.</p></abstract>

Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized (p, q)-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.

Fractional Calculus involving (<italic>p</italic>, <italic>q</italic>)-Mathieu Type Series

Anand International College of Engineering

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fractional Calculus involving (, )-Mathieu Type Series

Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized (p, q)-Mathieu type...

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

Published Online: Jul 01, 2020

Page range: 15 - 34

Received: May 04, 2019

Accepted: Jul 29, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00011

Keywords
Fractional integral operators, Fractional derivative operators, Extended generalized Mathieu series, Integral transforms

© 2020 Daljeet Kaur et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Jul 01, 2020

Page range: 15 - 34

Received: May 04, 2019

Accepted: Jul 29, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00011

KeywordsFractional integral operators, Fractional derivative operators, Extended generalized Mathieu series, Integral transforms

© 2020 Daljeet Kaur et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Fractional integral operators, Fractional derivative operators, Extended generalized Mathieu series, Integral transforms