Computing Eigenelements of Sturm–Liouville Problems of Fractional Order via Fractional Differential Transform Method

By V. S. Erturk. 2011

54 citations recorded by the source corpus.

In this study, fractional differential transform method (FDTM), which is a semi analytical-numerical technique, is used for computing the eigenelements of the Sturm-Liouville problems of fractional order. The fractional derivatives are described in the Caputo sense. Three problems are solved by the present method. The calculated results are compared closely with the results obtained by some existing techniques in literature. It is observed that FDTM can be utilized as an alternative tool for the solution of this type of problems.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/31f0c2b4e7f3d0958cc5e3252ee905b933663b35

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In Applied Mathematics

1. Mohamed Ali Hajji
2. G. Em Karniadakis
3. Mohsen Zayernouri
4. Q. Al‐Mdallal
5. Thabet Abdeljawad

In Modeling and Simulation

1. G. Em Karniadakis
2. Mohsen Zayernouri
3. Mohamed Ali Hajji
4. Q. Al‐Mdallal
5. Thabet Abdeljawad
6. Zhiping Mao

In Numerical Analysis

1. Mohamed Ali Hajji
2. Q. Al‐Mdallal
3. G. Em Karniadakis
4. Mohsen Zayernouri

Citations in the corpus

• Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation (2013, methodology): “In most of the fractional Sturm–Liouville formulations presented recently, the ordinary derivatives in a traditional Sturm–Liouville problem are replaced with fractional derivatives, and the resulting problems are solved using some numerical schemes such as Adomian decomposition method [9], or fract”
• A Convergent Algorithm for Solving Higher-Order Nonlinear Fractional Boundary Value Problems (2015, methodology): “These techniques include the Adomian’s decomposition method [33], the homotopy perturbation method [6, 3, 42], the variation iteration method [26], the variational iteration method considering Adomian’s polynomials approximation for nonlinear terms [23], the fractional differential transform method ”