Browsing by Author "Bas, Erdal"

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Citation - WoS: 33
Citation - Scopus: 33
Comparative Simulations for Solutions of Fractional Sturm-Liouville Problems With Non-Singular Operators
(Springeropen, 2018) Ozarslan, Ramazan; Baleanu, Dumitru; Ercan, Ahu; Bas, Erdal
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.
Citation - WoS: 29
Citation - Scopus: 27
Fractional Physical Problems Including Wind-Influenced Projectile Motion With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2020) Bas, Erdal; Baleanu, Dumitru; Acay, Bahar; Ozarslan, Ramazan
In this manuscript the fractional form of wind-influenced projectile motion equations which have a significant place in physics is extensively investigated by preserving dimensionality of the physical quantities for fractional operators and features of wind-influenced projectile motion are computed analytically in view of Atangana-Baleanu (ABC) fractional derivative in Caputo sense. Moreover, ABC fractional derivative with (n + alpha)th-order and its Laplace transform (LT) are obtained, alpha is an element of [0, 1] and n is an element of N. A comparative analysis based on the classical case is carried out in order to shed more light on the potent of the ABC fractional operator. Hence we present the results for some values of ff, k friction constant, different wind effects and different masses in 3D illustrations by comparing Caputo fractional operator. Thus, we can observe trajectory, time of flight, maximum height and range clearly. Moreover, the obtained results are shown to correspond to the classical case while the order alpha -> 1.
Citation - WoS: 14
Citation - Scopus: 12
Representation of Solutions for Sturm-Liouville Eigenvalue Problems With Generalized Fractional Derivative
(Amer inst Physics, 2020) Bas, Erdal; Baleanu, Dumitru; Ozarslan, Ramazan
We analyze fractional Sturm-Liouville problems with a new generalized fractional derivative in five different forms. We investigate the representation of solutions by means of rho-Laplace transform for generalized fractional Sturm-Liouville initial value problems. Finally, we examine eigenfunctions and eigenvalues for generalized fractional Sturm-Liouville boundary value problems. All results obtained are compared with simulations in detail under different alpha fractional orders and real rho values. Published under license by AIP Publishing.
Citation - WoS: 9
Citation - Scopus: 11
Sturm-Liouville Difference Equations Having Bessel and Hydrogen Atom Potential Type
(de Gruyter Poland Sp Zoo, 2018) Ozarslan, Ramazan; Baleanu, Dumitru; Bas, Erdal
In this work, we bring a different approach for Sturm-Liouville problems having Bessel and hydrogen atom type and we provide a basis for direct and inverse problems. From this point of view, we find representations of solutions and asymptotic expansions for eigenfunctions. Furthermore, some numerical estimations are given to illustrate the necessity of the Sturm-Liouville difference equations with the potential function for the convenience to the spectral theory. The behavior of eigenfunctions for the Sturm-Liouville problem having Bessel and hydrogen atom potential type is analyzed and compared to each other. And then, comparisons are showed by tables and figures.