First Step to Spectral Theory with Generalized M Derivative and Applications
Keywords:
Generalized M-derivative, Sturm-Liouville problem, Laplace transform, Direct problemAbstract
In this article, several fundamental spectral results are established for the Sturm–Liouville problem with discrete boundary conditions involving the generalized M-derivative. The paper is organized into four sections. The first section provides a brief historical background of the topic. The second section presents essential definitions and foundational theorems. In the third section, we investigate the uniqueness theorem for the generalized M-derivative Sturm–Liouville boundary value problem on a finite interval and offer two distinct methods for representing the solution. The final section offers a comprehensive evaluation of the study, including a detailed visual analysis using graphical illustrations.
References
Abdeljawad, T. (2015). On conformable fractional calculus. Journal of computational and Applied Mathematics, 279, 57-66.
Acay, B., Bas, E., Abdeljawad, T. (2020). Non-local fractional calculus from different viewpoint generated by truncated M-derivative. Journal of Computational and Applied Mathematics, 366, 112410.
Bas, E., Acay, B. (2020). The direct spectral problem via local derivative including truncated Mittag- Leffler function. Applied Mathematics and Computation, 367, 124787.
̇Ilhan, E., Kıymaz, ̇I. O. (2020). A generalization of truncated M-fractional derivative and applications to fractional differential equations. Applied Mathematics and Nonlinear Sciences, 5(1), 171-188.
Levitan, B. M., Sargsian, I. S. (1975). Introduction to spectral theory: selfadjoint ordinary differential operators (Vol. 39). American Mathematical Soc.
Miller, K. S., Ross, B. (1993). An Introduction to The Fractional Calculus and Fractional Differential Equations, John-Wily and Sons. Inc. New York.
Oldham, K., Spanier, J. (1974). The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier.
Podlubny, I. (1999). Fractional Differential Equations. Academic Press.
Sousa, J., Capelas de Oliveira, E. (2017). A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties. arXiv e-prints, arXiv- 1704.
Published
How to Cite
Issue
Section
Copyright (c) 1970 Merve Karaoglan, Erdal BAS
This work is licensed under a Creative Commons Attribution 4.0 International License.
