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Special functions with general kernel: Properties and applications to fractional partial differential equations Cover

Special functions with general kernel: Properties and applications to fractional partial differential equations

International Journal of Mathematics and Computer in Engineering
Volume 3 (2025): Issue 2 (December 2025)
By: Enes Ata and  İsmail Onur Kıymaz  
Open Access
|Sep 2024

Figures & Tables

Fig. 1

The approximate graphs of Eq. (51) for the values u = v = 0,1,2,3, κ = μ = 1, σ = τ = 3, 0 < p < 1, 0 < q < 4, ɛ1 = ɛ2 = 1.6 (yellow), ɛ1 = ɛ2 = 1.8 (blue) and ɛ1 = ɛ2 = 2 (green).
The approximate graphs of Eq. (51) for the values u = v = 0,1,2,3, κ = μ = 1, σ = τ = 3, 0 < p < 1, 0 < q < 4, ɛ1 = ɛ2 = 1.6 (yellow), ɛ1 = ɛ2 = 1.8 (blue) and ɛ1 = ɛ2 = 2 (green).

Fig. 2

The approximate graphs of Eq. (52) for the values u = v = k = 0,1,2,3, κ = μ = ϑ1 = 1, ϑ2 = 2, ϑ3 = 5, z = 0.5, 0 < p < 1, 0 < q < 4, ɛ1 = ɛ2 = 1.6 (yellow), ɛ1 = ɛ2 = 1.8 (blue) and ɛ1 = ɛ2 = 2 (green).
The approximate graphs of Eq. (52) for the values u = v = k = 0,1,2,3, κ = μ = ϑ1 = 1, ϑ2 = 2, ϑ3 = 5, z = 0.5, 0 < p < 1, 0 < q < 4, ɛ1 = ɛ2 = 1.6 (yellow), ɛ1 = ɛ2 = 1.8 (blue) and ɛ1 = ɛ2 = 2 (green).

Fig. 3

The approximate graphs of Eq. (53) for the values u = v = k = 0,1,2,3, κ = μ = 1, ϑ2 = 2, ϑ3 = 5, z = 0.5, 0 < p < 1, 0 < q < 4, ɛ1 = ɛ2 = 1.6 (yellow), ɛ1 = ɛ2 = 1.8 (blue) and ɛ1 = ɛ2 = 2 (green).
The approximate graphs of Eq. (53) for the values u = v = k = 0,1,2,3, κ = μ = 1, ϑ2 = 2, ϑ3 = 5, z = 0.5, 0 < p < 1, 0 < q < 4, ɛ1 = ɛ2 = 1.6 (yellow), ɛ1 = ɛ2 = 1.8 (blue) and ɛ1 = ɛ2 = 2 (green).
DOI: https://doi.org/10.2478/ijmce-2025-0013 | Journal eISSN: 2956-7068
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Language: English
Page range: 153 - 170
Submitted on: Oct 10, 2023
Accepted on: Feb 28, 2024
Published on: Sep 22, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
Laplace transform,
Fractional derivatives and integrals,
Fractional partial differential equations,
Gamma and Beta functions,
Gauss and Confluent hypergeometric functions
Related subjects:
Computer sciences,
Computer sciences, other,
Engineering,
Introductions and overviews,
Engineering, other,
Mathematics,
General mathematics,
Physics,
Physics, other

© 2024 Enes Ata, İsmail Onur Kıymaz, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

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