An efficient scheme for solving a system of fractional differential equations with boundary conditions

Hatipoğlu, Veysel Fuat; Alkan, Sertan; Seçer, Aydın

doi:10.1186/s13662-017-1260-9

Cited by 10 publications

(6 citation statements)

References 24 publications

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“…Now we have a linear system of with equations given by (9). The unknown coefficients can be determined by solving the system.…”

Section: The Sinc-collocation Methodsmentioning

confidence: 99%

“…Since then, fractional calculus developed mainly as a pure theoretical field for mathematicians. However, in the last few decades fractional calculus has fastinated the interest of many researchers in several areas [2][3][4][5][6][7][8][9]. Many mathematicians contributed to the development of fractional calculus, therefore many definitions for the fractional derivative are available In the last years, Khalil et al [10] identified a new definition of fractional derivative called the conformable fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

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A collocation method for solving boundary value problems of fractional order

Alkan

Seçer

2018

Sakarya University Journal of Science

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In this work, the Sinc-Collocation Method (SCM) is used to find the approximate solutions of the secondorder fractional boundary value problems based on the conformable fractional derivative. For this purpose, a theorem is proved to represent the terms having fractional derivatives in terms of sinc basis functions. To show the effectiveness and accuracy of the method, some special problems are handled and the determined solutions are compared with the approximate solutions arising from using the other numerical methods as well as the exact solutions of the problems.

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“…Now we have a linear system of with equations given by (9). The unknown coefficients can be determined by solving the system.…”

Section: The Sinc-collocation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A collocation method for solving boundary value problems of fractional order

Alkan

Seçer

2018

Sakarya University Journal of Science

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“…These kinds of systems are usually difficult to solve analytically, especially for singular, nonlinear, and nonhomogenous cases. To this end, extensive research has been carried out to obtain numerical schemes and various methods as utilized in the literature as follows: n [21], the authors applied the Adomian decomposition scheme; in [22], the authors described the sinc collocation algorithm; and in [23] the authors utilized the fractional Lagrangian approach.…”

Section: Introductionmentioning

confidence: 99%

Adaptation of the Novel Cubic B-Spline Algorithm for Dealing with Conformable Systems of Differential Boundary Value Problems concerning Two Points and Two Fractional Parameters

Arqub

Tayebi

Momani

et al. 2023

Journal of Function Spaces

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Recently, conformable calculus has appeared in many abstract uses in mathematics and several practical applications in engineering and science. In addition, many methods and numerical algorithms have been adapted to it. In this paper, we will demonstrate, use, and construct the cubic B-spline algorithm to deal with conformable systems of differential boundary value problems concerning two points and two fractional parameters in both regular and singular types. Here, several linear and nonlinear examples will be presented, and a model for the Lane-Emden will be one of the applications presented. Indeed, we will show the complete construction of the used spline through the conformable derivative along with the convergence theory, and the error orders together with other results that we will present in detail in the form of tables and graphs using Mathematica software. Through the results we obtained, it became clear to us that the spline approach is effective and fast, and it requires little compulsive and mathematical burden in solving the problems presented. At the end of the article, we presented a summary that contains the most important findings, what we calculated, and some future suggestions.

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“…Some of them are the Caputo derivative, the Riemann-Liouville derivative, Atangana-Baleanu-Caputo derivative, the Caputo-Fabrizio derivative, beta derivative and conformable derivative. Several applications for those derivatives are developed in references [3,4,5,6,7,8,9,10,11,12,13]. In this paper, conformable definition of fractional derivative defined in [14] is considered.…”

Section: Introductionmentioning

confidence: 99%

Approximate analytical solutions of a class of non-linear fractional boundary value problems with conformable derivative

Alkan

2021

THERM SCI

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In this paper, it is presented that an approximate solution of a class of nonlinear differential equations with conformable derivative under boundary conditions by using sinc-Galerkin method that is not used to approximately solve the class of the considered equation in the literature. In the method, the solution function is expressed as a finite series in terms of composite translated sinc functions and the unknown coefficients. The problem is reduced into a nonlinear matrix-vector system via sinc grid points, and when this system is solved by using Newton?s method, the unknown coefficients of the solution function are easily obtained. Also, error analysis and some test problems are presented to illustrate the applicability and accuracy of the proposed method.

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An efficient scheme for solving a system of fractional differential equations with boundary conditions

Cited by 10 publications

References 24 publications

A collocation method for solving boundary value problems of fractional order

A collocation method for solving boundary value problems of fractional order

Adaptation of the Novel Cubic B-Spline Algorithm for Dealing with Conformable Systems of Differential Boundary Value Problems concerning Two Points and Two Fractional Parameters

Approximate analytical solutions of a class of non-linear fractional boundary value problems with conformable derivative

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