Journal ArticleDOI
On the numerical solution of fractional Sturm-Liouville problems
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It is shown briefly that this class of eigenvalue could be very promising to the solution of linear fractional partial differential equations of Sturm-Liouville problems.Abstract:
The differential equation of Sturm-Liouville problems is generalized into fractional form by replacing the first-order derivative by a fractional derivative of order α, 0<α≤1. We showed briefly that this class of eigenvalue could be very promising to the solution of linear fractional partial differential equations. The homotopy perturbation method is considered for computing the eigenelements of the present problem. Based on our simulations some theoretical conjectures are reported.read more
Citations
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Journal ArticleDOI
Fractional Sturm-Liouville problem
Malgorzata Klimek,Om P. Agrawal +1 more
TL;DR: It is shown that the Legendre Polynomials resulting from an FLE are the same as those obtained from the integer order Legendre equation; however, the eigenvalues of the two equations differ.
Journal ArticleDOI
Fractional logistic models in the frame of fractional operators generated by conformable derivatives
TL;DR: In this article, the existence and uniqueness theorems to solutions of these models and discuss their stability by perturbing the equilibrium points are discussed and illustrated by illustrative numerical examples for the studied models.
Journal ArticleDOI
A collocation-shooting method for solving fractional boundary value problems
TL;DR: In this paper, the numerical solution of a special class of fractional boundary value problems of order 2 is discussed, which is based on a conjugating collocation and spline analysis combined with shooting method.
Journal ArticleDOI
On the asymptotic stability of linear system of fractional-order difference equations
TL;DR: In this article, the stability of the equilibrium solution of the νth order linear system of difference equations was investigated, where 0 < ν < 1 and y−1 ∈ ℝp.
Journal ArticleDOI
Discrete Mittag-Leffler kernel type fractional difference initial value problems and Gronwall’s inequality
TL;DR: This article studied the Caputo and Riemann–Liouville type discrete fractional difference initial value problems with discrete Mittag-Leffler kernels to prove the existence and uniqueness of the solution and the Gronwall’s inequality under a new defined α -Lipschitzian.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Journal ArticleDOI
Application of differential transformation to eigenvalue problems
Cha'o-Kuang Chen,Shing-Huei Ho +1 more
TL;DR: Using differential transformation to solve eigenvalue problems is introduced in this paper, where two eigen value problems are solved by the present method and the calculated results are compared closely with the results obtained by another analytical method.
Journal ArticleDOI
On solving some eigenvalue problems by using a differential transformation
TL;DR: This paper deals with eigenvalues and normalized eigenfunctions for a Sturm-Liouville eigenvalue problem and compared the results with some known analytical results.
Journal ArticleDOI
Derivation of the Adomian decomposition method using the homotopy analysis method
TL;DR: The mathematical derivation of the Adomian decomposition method using the homotopy analysis method is presented and an error analysis is addressed as well as the convergence criteria.