Kernel functions‐based approach for distributed order diffusion equations

Geng, Fazhan; Wu, Xinyuan

doi:10.1002/num.22578

Cited by 5 publications

(1 citation statement)

References 41 publications

(53 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where α > 0 denotes the order of the integral. This new fractional derivative is drawing the attention of many researchers in various branches of science and, as a result, there is a substantial amount of study in the literature such as on the hybrid fractional derivative [2][3][4][5][6], heat and mass transportation [7][8][9][10] and dynamics of processes [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Solution of hybrid time fractional diffusion problem via weighted inner product

Çetınkaya¹,

Demir²

2021

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

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.

show abstract