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Representation of solutions for Sturm-Liouville eigenvalue problems with generalized fractional derivative
Ramazan Ozarslan1, Erdal Bas1, Dumitru Baleanu2
1Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey.
Chaos (Woodbury, N.Y.)
|April 3, 2020
Summary
This study introduces a novel generalized fractional derivative to analyze fractional Sturm-Liouville problems. Researchers explored solutions using the ρ-Laplace transform and examined eigenvalues and eigenfunctions for these problems.
Area of Science:
- Mathematics
- Applied Mathematics
- Fractional Calculus
Background:
- Fractional Sturm-Liouville problems are essential in various scientific fields.
- Existing methods may not fully capture the complexities of generalized fractional derivatives.
Purpose of the Study:
- To analyze fractional Sturm-Liouville problems using a new generalized fractional derivative.
- To investigate the ρ-Laplace transform for solving initial value problems.
- To examine eigenfunctions and eigenvalues for boundary value problems.
Main Methods:
- Analysis of fractional Sturm-Liouville problems with five forms of a new generalized fractional derivative.
- Application of the ρ-Laplace transform for generalized fractional Sturm-Liouville initial value problems.
- Examination of eigenfunctions and eigenvalues for generalized fractional Sturm-Liouville boundary value problems.
Main Results:
- The study presents a novel framework for analyzing generalized fractional Sturm-Liouville problems.
- The ρ-Laplace transform is shown to be effective for representing solutions.
- Eigenfunctions and eigenvalues were systematically investigated and compared with simulations.
Conclusions:
- The proposed generalized fractional derivative offers a new perspective on fractional calculus.
- The ρ-Laplace transform provides a valuable tool for solving these complex problems.
- Simulations confirm the validity of the theoretical findings across various parameters.
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