The Analytic Solution of Initial Boundary Value Problem Including Time Fractional Diffusion Equation

Çetınkaya, Süleyman; Demir, Ali; Sevindir, Hülya Kodal

doi:10.22190/fumi2001243c

Cited by 8 publications

(8 citation statements)

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“…(16) leads to the solution of the problem (Eqs. (11)(12)(13)) which implies the correctness of the method employed in this study.…”

Section: Thus (16)mentioning

confidence: 57%

“…This mathematical modelling describes the behaviour of matter in a phase. There are many published works on the diffusion of various matters in science especially in fluid mechanics and gas dynamics [3][4][5][6][7][8][9][10][11][12][13][14]. From this aspect, analysis of this problem plays an important role in application.…”

Section:  and mentioning

confidence: 99%

“…It is clear from Eq. (10) that the solution to the above problem can be obtained in the following form:  As in Example 1, after similar computations the solution can be constructed as follows:The graphics of solutions for Example 1, Example 2, and the problem (Eqs (11)(12)(13)…”

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confidence: 99%

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Equation Including Local Fractional Derivative and Neumann Boundary Conditions

Çetınkaya

Demir

2020

Kocaeli Journal of Science and Engineering

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The aim of this study to discuss the construction of solution of fractional partial differential equations (FPDEs) with initial and boundary conditions. Since the homogenous initial boundary value problem involves local fractional-order derivative, it has classical initial and boundary conditions. By means of the separation of variables method (SVM) and the inner product on , we construct the solution in this series form in terms of eigenfunctions of related Sturm-Liouville problem. An illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.

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“…(16) leads to the solution of the problem (Eqs. (11)(12)(13)) which implies the correctness of the method employed in this study.…”

Section: Thus (16)mentioning

confidence: 57%

Section:  and mentioning

confidence: 99%

See 1 more Smart Citation

Equation Including Local Fractional Derivative and Neumann Boundary Conditions

Çetınkaya

Demir

2020

Kocaeli Journal of Science and Engineering

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“…Mathematical models by fractional differential equations for various physical phenomena play important roles in all applied sciences such as mathematics physics, biology, dynamical systems, control systems, engineering and so on [1,2,3,4,5,6,7,8,9,10,11,12]. Also, there are various studies on fractional diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Nonlinear Fractional Differential Equations via Laplace Transform

Çetınkaya

Demir

2021

FU Math Inform

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“…This mathematical modelling describes the behaviour of matter in a phase. There is a vast amount of published work on the diffusion of various matters in science, especially in fluid mechanics and gas dynamics [16][17][18][19]. From this aspect, the analysis of this problem plays an important role in its application.…”

Section: Introductionmentioning

confidence: 99%

Solution of hybrid time fractional diffusion problem via weighted inner product

Çetınkaya¹,

Demir²

2021

J. Appl. Math. Comput. Mech.

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In this research, we discuss the construction of the analytic solution of homogenous initial boundary value problem including partial differential equations of fractional order. Since the homogenous initial boundary value problem involves the Hybrid fractional order derivative with various coefficients functions, it has classical initial and boundary conditions. By means of separation of the variables method and the inner product defined on L 2 [0, l], the solution is constructed in the form of a Fourier series including the bivariate Mittag-Leffler function. An illustrative example presents the applicability and influence of the separation of variables method on time fractional diffusion problems. Moreover, as the fractional order α tends to 1, the solution of the fractional diffusion problem tends to the solution of the diffusion problem which proves the accuracy of the solution.

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The Analytic Solution of Initial Boundary Value Problem Including Time Fractional Diffusion Equation

Cited by 8 publications

References 0 publications

Equation Including Local Fractional Derivative and Neumann Boundary Conditions

Equation Including Local Fractional Derivative and Neumann Boundary Conditions

Numerical Solutions of Nonlinear Fractional Differential Equations via Laplace Transform

Solution of hybrid time fractional diffusion problem via weighted inner product

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