Some dynamical models involving fractional-order derivatives with the Mittag-Leffler type kernels and their applications based upon the Legendre spectral collocation method

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dc.contributor.authorSrivastava, H.M.
dc.contributor.authorAlomari, Abedel-Karrem N.
dc.contributor.authorSaad, Khaled M.
dc.contributor.authorHamanah, Waleed M.
dc.date.accessioned2022-11-15T23:35:22Z
dc.date.available2022-11-15T23:35:22Z
dc.date.copyright2021en_US
dc.date.issued2021
dc.description.abstractFractional derivative models involving generalized Mittag-Leffler kernels and opposing models are investigated. We first replace the classical derivative with the GMLK in order to obtain the new fractional-order models (GMLK) with the three parameters that are investigated. We utilize a spectral collocation method based on Legendre’s polynomials for evaluating the numerical solutions of the pr. We then construct a scheme for the fractional-order models by using the spectral method involving the Legendre polynomials. In the first model, we directly obtain a set of nonlinear algebraic equations, which can be approximated by the Newton-Raphson method. For the second model, we also need to use the finite differences method to obtain the set of nonlinear algebraic equations, which are also approximated as in the first model. The accuracy of the results is verified in the first model by comparing it with our analytical solution. In the second and third models, the residual error functions are calculated. In all cases, the results are found to be in agreement. The method is a powerful hybrid technique of numerical and analytical approach that is applicable for partial differential equations with multi-order of fractional derivatives involving GMLK with three parameters.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.identifier.citationSrivastava, H. M., Alomari, A. N., Saad, K. M., & Hamanah, W. M. (2021). “Some dynamical models involving fractional-order derivatives with the Mittag-Leffler type kernels and their applications based upon the Legendre spectral collocation method.” Fractal and Fractional, 5(3), 131. https://doi.org/10.3390/fractalfract5030131en_US
dc.identifier.urihttps://doi.org/10.3390/fractalfract5030131
dc.identifier.urihttp://hdl.handle.net/1828/14471
dc.language.isoenen_US
dc.publisherFractal and Fractionalen_US
dc.subjectfractional derivative
dc.subjectgeneralized Mittag-Leffler kernel (GMLK)
dc.subjectLegendre polynomials
dc.subjectLegendre spectral collocation method
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleSome dynamical models involving fractional-order derivatives with the Mittag-Leffler type kernels and their applications based upon the Legendre spectral collocation methoden_US
dc.typeArticleen_US

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