α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator

Esengül Koç; Yaşar Çakmak

doi:10.17776/csj.1208016

EN

α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator

Abstract

In this paper, we consider a diffusion operator which includes conformable fractional derivatives of order α (0<α≤1) instead of the ordinary derivatives in a traditional diffusion operator. We give an α-integral representation for the solution of this operator and obtain the conditions provided by the kernel functions in this representation. Also, by investigating the basic properties of this operator, we obtain the asymptotics of the data {λ_n,α_n }, which are called the spectral data of the operator.

Keywords

Diffusion operator, Integral representation, Conformable fractional derivative, Spectral data

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Esengül Koç This is me
0000-0002-9565-5266
Türkiye

Yaşar Çakmak ^*
0000-0002-6820-1322
Türkiye

Publication Date

March 26, 2023

Submission Date

November 21, 2022

Acceptance Date

March 6, 2023

Published in Issue

Year 2023 Volume: 44 Number: 1

DOI

https://doi.org/10.17776/csj.1208016

IZ

https://izlik.org/JA79CB64JB

APA

Koç, E., & Çakmak, Y. (2023). α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator. Cumhuriyet Science Journal, 44(1), 170-180. https://doi.org/10.17776/csj.1208016

AMA

1.Koç E, Çakmak Y. α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator. CSJ. 2023;44(1):170-180. doi:10.17776/csj.1208016

Chicago

Koç, Esengül, and Yaşar Çakmak. 2023. “α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator”. Cumhuriyet Science Journal 44 (1): 170-80. https://doi.org/10.17776/csj.1208016.

EndNote

Koç E, Çakmak Y (March 1, 2023) α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator. Cumhuriyet Science Journal 44 1 170–180.

IEEE

[1]E. Koç and Y. Çakmak, “α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator”, CSJ, vol. 44, no. 1, pp. 170–180, Mar. 2023, doi: 10.17776/csj.1208016.

ISNAD

Koç, Esengül - Çakmak, Yaşar. “α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator”. Cumhuriyet Science Journal 44/1 (March 1, 2023): 170-180. https://doi.org/10.17776/csj.1208016.

JAMA

1.Koç E, Çakmak Y. α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator. CSJ. 2023;44:170–180.

MLA

Koç, Esengül, and Yaşar Çakmak. “α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator”. Cumhuriyet Science Journal, vol. 44, no. 1, Mar. 2023, pp. 170-8, doi:10.17776/csj.1208016.

Vancouver

1.Esengül Koç, Yaşar Çakmak. α-Integral Representation of The Solution for A Conformable Fractional Diffusion Operator and Basic Properties of The Operator. CSJ. 2023 Mar. 1;44(1):170-8. doi:10.17776/csj.1208016

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Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator

Communications in Advanced Mathematical Sciences

https://doi.org/10.33434/cams.1281434

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