2019
DOI: 10.19113/sdufenbed.579361
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Numerical Solutions of Conformable Fractional Differential Equations by Taylor and Finite Difference Methods

Abstract: We drive efficient and reliable finite difference methods for fractional differential equations (FDEs) based on recently defined conformable fractional derivative. We first derive fractional Euler and fractional Taylor methods based on the fractional Taylor expansion. This fractional Taylor series are the generalized fractional Taylor series that are independent of initial point. We show that the proposed methods are more efficient and faster by applying these methods on first order FDEs and second order oscil… Show more

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Cited by 12 publications
(8 citation statements)
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“…So, equations ( 4) and (5) show that error equation obtained by both Taylor series (the classical one, and that provided in [6]) is the same.…”
Section: Remarkmentioning
confidence: 83%
See 2 more Smart Citations
“…So, equations ( 4) and (5) show that error equation obtained by both Taylor series (the classical one, and that provided in [6]) is the same.…”
Section: Remarkmentioning
confidence: 83%
“…In [5], the quadratic convergence of this method by using a suitable conformable Taylor series (see [6]) is stated by the next result.…”
Section: Introductionmentioning
confidence: 91%
See 1 more Smart Citation
“…In Ref. [20], an appropriate conformable Taylor series is provided, as shown in the following result.…”
Section: Introductionmentioning
confidence: 99%
“…Theorem 1 (Theorem 4.1, [20]). Let f (x) be an infinitely α-differentiable function, α ∈ (0, 1], about a 1 , where the conformable derivatives start at a.…”
Section: Introductionmentioning
confidence: 99%