Numerical Solution of Fractional Differential Equations by using Fractional Spline Functions.

Hamasalh, Faraidun K.; Muhammad, Pshtiwan O.

doi:10.17656/jzs.10404

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…2006;Diethelm, K. 2010;Hamasalh F. K., & Mohammed, P. O. 2015a;Hamasalh F. K., & Mohammed, P. O. 2015b).…”

Section: Introductionmentioning

confidence: 99%

A Generalized Uncertain Fractional Forward Difference Equations of Riemann-Liouville Type

Mohammed¹

2019

JMR

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In this paper, we firstly recall the definition of an uncertain fractional forward difference equation with Riemann-Liouvillelike forward difference. After that analytic solutions to a generalized uncertain fractional difference equations are solved by using the Picard successive iteration method. Moreover, the existence and uniqueness theorem of the solutions are proved by applying Banach contraction mapping theorem. Finally, two examples are presented to illustrate the validity of the existence and uniqueness theorem.

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“…2006;Diethelm, K. 2010;Hamasalh F. K., & Mohammed, P. O. 2015a;Hamasalh F. K., & Mohammed, P. O. 2015b).…”

Section: Introductionmentioning

confidence: 99%

A Generalized Uncertain Fractional Forward Difference Equations of Riemann-Liouville Type

Mohammed¹

2019

JMR

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“…2! ∥ 𝑓 (6) (𝑥) ∥ , and since 𝑓 (𝑝) (0) = 0, 𝑝 = 1,2, also using [23], clearly find the error estimation as follows following:…”

Section: Theorem 31mentioning

confidence: 85%

Optimized Trigonometric Spline Function with Conjugate GradientMethod for Solving FDEs

Hamasalh¹,

Sadiq²,

Salam³

2022

JUAPS

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We investigate the non-polynomial spline function to solve the fractional differential equations with the conformable conjugate gradient method. The fractional derivative was described using the Caputo fractional derivative to construct the spline scheme with polynomial fractional order. Therefore, transform the problem to an equivalent iterative linear system that can be solved by Gauss-Seidel and conjugate gradient methods. For the given spline function, error bounds were studied and a stability analysis was completed, the error estimation is also calculated as different values of (n) depend on the step size oh (h). Numerical examples with known analytical solutions are shown to verify the method's accuracy. The outcomes are in satisfactory correlation with the exact answers according to the numerical experiments. Moreover, the convergence analysis was investigated with the drive some theorems. Also, the procedure is explained in depth and supported by computational examples and the results show that the fractional spline function which interpolates data is productive and profitable in solving unique problems and compare with the exact solutions.

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The applications of non-polynomial spline to the numerical solution for fractional differential equations

Hamasalh

Headayat²

2021

Fourth International Conference of Mathematical Sciences (Icms 2020)

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Numerical Solution of Fractional Differential Equations by using Fractional Spline Functions.

Cited by 3 publications

References 12 publications

A Generalized Uncertain Fractional Forward Difference Equations of Riemann-Liouville Type

A Generalized Uncertain Fractional Forward Difference Equations of Riemann-Liouville Type

Optimized Trigonometric Spline Function with Conjugate GradientMethod for Solving FDEs

The applications of non-polynomial spline to the numerical solution for fractional differential equations

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