Comparative Simulations for Solutions of Fractional Sturm-Liouville Problems With Non-Singular Operators
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Date
2018
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Springeropen
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GOLD
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No
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Top 10%
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Abstract
In this study, we consider fractional Sturm-Liouville (S-L) problems within non-singular operators. A fractional S-L problem with exponential and Mittag-Leffler kernels is given with different versions in the Riemann-Liouville and Caputo sense. Also, we obtain representation of solutions for S-L problems by the Laplace transform and find analytical solutions of the problems. Finally, we compare the solutions of the problem with these different versions, and we also compare the solutions of the problem with exponential and Mittag-Leffler kernels together by simulation under different potentials, different orders, and different eigenvalues.
Description
Bas, Erdal/0000-0002-7285-7308; Ercan, Ahu/0000-0001-6290-2155; Ozarslan, Ramazan/0000-0002-2275-8061
Keywords
Sturm-Liouville, Fractional Operator, Exponential Kernel, Mittag-Leffler Kernel, Laplace Transform, Laplace transform, Spectral Theory of Differential Operators, Mathematical analysis, Quantum mechanics, Sturm–Liouville theory, Differential equation, Inverse Spectral Problems, Mittag-Leffler kernel, QA1-939, FOS: Mathematics, Singular solution, Boundary value problem, Anomalous Diffusion Modeling and Analysis, Mathematical Physics, Eigenvalues and eigenvectors, Exponential kernel, Applied Mathematics, Physics, Exponential function, Fractional calculus, Pure mathematics, Partial differential equation, Applied mathematics, Nonlocal Partial Differential Equations and Boundary Value Problems, Fractional Derivatives, Modeling and Simulation, Physical Sciences, Fractional operator, Sturm–Liouville, Mathematics, Ordinary differential equation, exponential kernel, Fractional ordinary differential equations, Sturm-Liouville theory, Fractional derivatives and integrals, fractional operator
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Citation
Bas, Erdal; Ozarslan, Ramazan; Baleanu, Dumitru; et al. (2018).Comparative simulations for solutions of fractional Sturm-Liouville problems with non-singular operators, Advances in Difference Equations.
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Q1
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OpenCitations Citation Count
24
Source
Advances in Difference Equations
Volume
2018
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CrossRef : 4
Scopus : 32
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