Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

Lata Chanchlani; Pratibha Manohar; Ajay Sharma; Sangeeta Choudhary

doi:10.17485/IJST/v17i16.2514

Article

Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i16.2514

Year: 2024, Volume: 17, Issue: 16, Pages: 1702-1712

Original Article

Solution of Fractional Differential Equations Involving Hilfer-Hadamard Fractional Derivatives

Lata Chanchlani¹, Pratibha Manohar^2*, Ajay Sharma³, Sangeeta Choudhary⁴

¹Assistant Professor, Department of Mathematics, University of Rajasthan, Jaipur, 302004, Rajasthan, India
²Assistant Professor, Department of Statistics, Mathematics and Computer Science, SKN Agriculture University, Jobner, Jaipur, 303329, Rajasthan, India
³Assistant Professor, Department of Science and Humanities, Government Polytechnic College, Sikar, 332001, Rajasthan, India
⁴Associate Professor, Department of Mathematics, Swami Keshvanand Institute of Technology Management and Gramothan, Jaipur, 302017, Rajasthan, India

*Corresponding Author
Email: [email protected]

Received Date:26 October 2023, Accepted Date:08 March 2024, Published Date:19 April 2024

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

Abstract

Objectives: The aim is to establish prerequisite properties for the Hilfer-Hadamard fractional derivatives and address boundary value problems related to fractional polar Laplace and fractional Sturm-Liouville equations involving Hilfer-Hadamard fractional derivatives. Methods: Existing definitions and findings are utilized to obtain the properties for fractional derivatives, and the Adomian decomposition method is employed to solve the fractional differential equations. Findings: Validity conditions for the law of exponents are determined, and the study investigates the fractional differential equations and their corresponding solutions, possessing the capacity to replace the traditional polar Laplace and Sturm-Liouville boundary value problems to effectively represent real-world phenomena. Novelty: The study introduces the substitution of two consecutively operated Hilfer-Hadamard fractional derivatives with a corresponding single Hilfer-Hadamard fractional derivative using the law of exponents. Additionally, the polar Laplace and Sturm-Liouville boundary value problems are extended to their respective fractional counterparts, expressed in a concise format using HilferHadamard fractional derivatives.

Keywords: Adomian decomposition method, Hilfer-Hadamard fractional derivative, Fractional polar Laplace equation, Fractional Sturm-Liouville boundary value problem

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Copyright

© 2024 Chanchlani et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)