Efficient Mittag-Leffler Collocation Method for Solving Linear and Nonlinear Fractional Differential Equations

Rida, S. Z.; Hussein, Hussein S.

doi:10.1007/s00009-018-1174-0

Cited by 7 publications

(5 citation statements)

References 19 publications

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“…We take the first n-terms of the two-parameters MLF to obtain the so-called finite MLF2 in the following approximation form 26 :…”

Section: Finite Mlfs and Its Fractional Derivativementioning

confidence: 99%

“…Theorem 1. Suppose that 𝜑(t) ∈ C ∞ [0, 1] and approximated by 𝜑 n (t) as in the finite series (26), then for every 0 ≤ t ≤ 1, there exists 0 ≤ z ≤ 1, such that the error can be bounded by…”

Section: Finite Mlfs and Its Fractional Derivativementioning

confidence: 99%

“…We take the first n ‐terms of the two‐parameters MLF to obtain the so‐called finite MLF2 in the following approximation form 26 :

M_{n}^{ℓ, ℏ} false(t false) = true \sum_{i = 0}^{n} \frac{t^{i}}{normalΓ false(i ℓ + ℏ false)}, ℓ > 0, ℏ > 0, t \in ℝ .

…”

Section: Finite Mlfs and Its Fractional Derivativementioning

confidence: 99%

“…It arises nowadays in many applications such as fractional diffusion and relaxation problems 25 . Rida and Hussien 26 have developed a good approximation for solving FDEs with MLF as a basis, where they investigated the derivative of any fractional‐order of these functions. They developed procedures for solving the nonlinear fractional ODEs by combining the Mittag–Leffler collocation method (MLCM) and optimization technique.…”

Section: Introductionmentioning

confidence: 99%

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Mittag–Leffler collocation optimization method for studying a physical problem in fluid flow with fractional derivatives

Khader

2021

Math Methods in App Sciences

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An efficient computational approach is presented to solve numerically a mathematical model of fractional order in a fluid. The proposed model describes the effects of variable heat flux, viscous dissipation, and the slip velocity on the viscous Casson flow and heat transfer due to an unsteady stretching sheet taking into account the influence of heat generation or absorption. A collocation method based on a summation of Mittag-Leffler functions is employed to convert the system of ODEs that describe the problem to a system of algebraic equations. This system is constructed as a constrained optimization problem and optimized to get the unknown coefficients. Error analysis of the approximation solution is studied. The influence of the parameters governing the flow and heat transfer such as unsteadiness parameter, slip velocity parameter, Casson parameter, local Eckert number, heat generation parameter, and the Prandtl number are discussed and presented through tables and graphs. Besides, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed. Finally, the results show that the given procedure is an easy and efficient tool to investigate the solution of such fluid models.

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“…We take the first n-terms of the two-parameters MLF to obtain the so-called finite MLF2 in the following approximation form 26 :…”

Section: Finite Mlfs and Its Fractional Derivativementioning

confidence: 99%

Section: Finite Mlfs and Its Fractional Derivativementioning

confidence: 99%

“…We take the first n ‐terms of the two‐parameters MLF to obtain the so‐called finite MLF2 in the following approximation form 26 :

M_{n}^{ℓ, ℏ} false(t false) = true \sum_{i = 0}^{n} \frac{t^{i}}{normalΓ false(i ℓ + ℏ false)}, ℓ > 0, ℏ > 0, t \in ℝ .

…”

Section: Finite Mlfs and Its Fractional Derivativementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mittag–Leffler collocation optimization method for studying a physical problem in fluid flow with fractional derivatives

Khader

2021

Math Methods in App Sciences

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“…where M k (t) = Θ k t 0 E k (z, µ, ν)dz, is the Mittag operational matrix of integration. This approximation of integrals is accurate and highly efficient depending on the error analysis and results of Mittag-Leffler approximation [23].…”

Section: Mittag-leffler Function Approximation Of Integralsmentioning

confidence: 99%

Fractional Integro-Differential Equations With Nonlocal Conditions and Ψ–hilfer Fractional Derivative

Abdo

Panchal

Hussein

2019

Mathematical Modelling and Analysis

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Considering a fractional integro-differential equation with nonlocal conditions involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem and Krasnoselskii's fixed point theorem. An example is provided to illustrate our main results.

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An Iterative Approach for the Numerical Solution of Fractional BVPs

Alchikh

Khuri

2019

Int. J. Appl. Comput. Math

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Efficient Mittag-Leffler Collocation Method for Solving Linear and Nonlinear Fractional Differential Equations

Cited by 7 publications

References 19 publications

Mittag–Leffler collocation optimization method for studying a physical problem in fluid flow with fractional derivatives

Mittag–Leffler collocation optimization method for studying a physical problem in fluid flow with fractional derivatives

Fractional Integro-Differential Equations With Nonlocal Conditions and Ψ–hilfer Fractional Derivative

An Iterative Approach for the Numerical Solution of Fractional BVPs

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