Research Article
Year 2023,
, 170 - 180, 26.03.2023
Abstract
References
- [1] Khalil R., Al Horania M., Yousefa A., et al., A New Definition of Fractional Derivative, J. Comput. Appl. Math., 264 (2014) 65-70.
- [2] Abdeljawad T., On Conformable Fractional Calculus, J. Comput. Appl. Math., 279 (2015) 57-66.
- [3] Atangana A., Baleanu D., Alsaedi A., New Properties of Conformable Derivative, Open Math., 13 (2015) 889-898.
- [4] Abu Hammad M., Khalil R., Abel’s Formula and Wronskian for Conformable Fractional Differential Equations, Int. J. Differ. Equ. Appl., 13 (3) (2014) 177-183.
- [5] Birgani O.T., Chandok S., Dedovic N., Radenoviç S., A Note on Some Recent Results of the Conformable Derivative, Adv. Theory Nonlinear Anal. Appl., 3 (1) (2019) 11-17.
- [6] Zhao D., Luo M., General Conformable Fractional Derivative and its Physical Interpretation, Calcolo, 54 (2017) 903–917
- [7] Zhou H.W., Yang S., Zhang S.Q., Conformable Derivative Approach to Anomalous Diffusion, Physica A, 491 (2018) 1001-1013.
- [8] Chung W.S., Fractional Newton Mechanics with Conformable Fractional Derivative, J. Comput. Appl. Math., 290 (2015) 150-158.
- [9] Benkhettou N., Hassani S., Torres D.F.M., A Conformable Fractional Calculus on Arbitrary Time Scales, J. King Saud Univ. Sci., 28 (2016) 93–98.
- [10] Jarad F., Uğurlu E., Abdeljawad T., Baleanu D., On a New Class of Fractional Operators, Adv. in Differ. Equ., 2017 (2017) Article ID 247 .
- [11] Mortazaasl H., Jodayree Akbarfam A,. Trace Formula and Inverse Nodal Problem for a Conformable Fractional Sturm-Liouville Problem, Inverse Problems in Science and Engineering, 28 (4) (2020) 524-555.
- [12] Keskin B., Inverse Problems for one Dimentional Conformable Fractional Dirac Type Integro Differential System, Inverse Problems, 36 (6) (2020) 065001.
- [13] Adalar I., Ozkan A.S., Inverse Problems for a Conformable Fractional Sturm-Liouville Operators, Journal of Inverse and Ill-posed Problems, 28 (6) (2020).
- [14] Çakmak Y., Inverse Nodal Problem for a Conformable Fractional Diffusion Operator, Inverse Problems in Science and Engineering, 29 (9) (2021) 1308-1322.
- [15] Allahverdiev B.P., Tuna H., Yalçinkaya Y., Conformable Fractional Sturm-Liouville Equation, Mathematical Methods in the Applied Sciences, 42 (10) (2019) 3508-3526.
- [16] Gasymov M.G., Gusejnov G.S., Determination of a Diffusion Operator from Spectral Data, Akad. Nauk Azerb. SSR. Dokl., 37 (2) (1981) 19-23.
- [17] Koyunbakan H., Panakhov E.S., Half-Inverse Problem for Diffusion Operators on the Finite Interval, J. Math. Anal. Appl., 326 (2) (2007) 1024-1030.
- [18] Yang C.F., New Trace Formulae for a Quadratic Pencil of the Schrodinger Operator, Journal of Mathematical Physics, 51 (3) (2010) 33506-33506-10.
- [19] Wang Y., Zhou J., Li Y., Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales, Adv. Math. Phys., 2016 (2016) 21.
- [20]Guseinov G.Sh., Inverse Spectral Problems for a Quadratic Pencil of Sturm-Liouville Operators on a Finite Interval, Spectral Theory of Operators and Its Applications, Elm, Baku, Azerbaijan, 7, (1986) 51–101. (In Russian)
- [21] Freiling G., Yurko V.A., Inverse Sturm–Liouville Problems and Their Applications, New York: Nova Science Publishers, (2001).
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.
References
- [1] Khalil R., Al Horania M., Yousefa A., et al., A New Definition of Fractional Derivative, J. Comput. Appl. Math., 264 (2014) 65-70.
- [2] Abdeljawad T., On Conformable Fractional Calculus, J. Comput. Appl. Math., 279 (2015) 57-66.
- [3] Atangana A., Baleanu D., Alsaedi A., New Properties of Conformable Derivative, Open Math., 13 (2015) 889-898.
- [4] Abu Hammad M., Khalil R., Abel’s Formula and Wronskian for Conformable Fractional Differential Equations, Int. J. Differ. Equ. Appl., 13 (3) (2014) 177-183.
- [5] Birgani O.T., Chandok S., Dedovic N., Radenoviç S., A Note on Some Recent Results of the Conformable Derivative, Adv. Theory Nonlinear Anal. Appl., 3 (1) (2019) 11-17.
- [6] Zhao D., Luo M., General Conformable Fractional Derivative and its Physical Interpretation, Calcolo, 54 (2017) 903–917
- [7] Zhou H.W., Yang S., Zhang S.Q., Conformable Derivative Approach to Anomalous Diffusion, Physica A, 491 (2018) 1001-1013.
- [8] Chung W.S., Fractional Newton Mechanics with Conformable Fractional Derivative, J. Comput. Appl. Math., 290 (2015) 150-158.
- [9] Benkhettou N., Hassani S., Torres D.F.M., A Conformable Fractional Calculus on Arbitrary Time Scales, J. King Saud Univ. Sci., 28 (2016) 93–98.
- [10] Jarad F., Uğurlu E., Abdeljawad T., Baleanu D., On a New Class of Fractional Operators, Adv. in Differ. Equ., 2017 (2017) Article ID 247 .
- [11] Mortazaasl H., Jodayree Akbarfam A,. Trace Formula and Inverse Nodal Problem for a Conformable Fractional Sturm-Liouville Problem, Inverse Problems in Science and Engineering, 28 (4) (2020) 524-555.
- [12] Keskin B., Inverse Problems for one Dimentional Conformable Fractional Dirac Type Integro Differential System, Inverse Problems, 36 (6) (2020) 065001.
- [13] Adalar I., Ozkan A.S., Inverse Problems for a Conformable Fractional Sturm-Liouville Operators, Journal of Inverse and Ill-posed Problems, 28 (6) (2020).
- [14] Çakmak Y., Inverse Nodal Problem for a Conformable Fractional Diffusion Operator, Inverse Problems in Science and Engineering, 29 (9) (2021) 1308-1322.
- [15] Allahverdiev B.P., Tuna H., Yalçinkaya Y., Conformable Fractional Sturm-Liouville Equation, Mathematical Methods in the Applied Sciences, 42 (10) (2019) 3508-3526.
- [16] Gasymov M.G., Gusejnov G.S., Determination of a Diffusion Operator from Spectral Data, Akad. Nauk Azerb. SSR. Dokl., 37 (2) (1981) 19-23.
- [17] Koyunbakan H., Panakhov E.S., Half-Inverse Problem for Diffusion Operators on the Finite Interval, J. Math. Anal. Appl., 326 (2) (2007) 1024-1030.
- [18] Yang C.F., New Trace Formulae for a Quadratic Pencil of the Schrodinger Operator, Journal of Mathematical Physics, 51 (3) (2010) 33506-33506-10.
- [19] Wang Y., Zhou J., Li Y., Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales, Adv. Math. Phys., 2016 (2016) 21.
- [20]Guseinov G.Sh., Inverse Spectral Problems for a Quadratic Pencil of Sturm-Liouville Operators on a Finite Interval, Spectral Theory of Operators and Its Applications, Elm, Baku, Azerbaijan, 7, (1986) 51–101. (In Russian)
- [21] Freiling G., Yurko V.A., Inverse Sturm–Liouville Problems and Their Applications, New York: Nova Science Publishers, (2001).
There are 21 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | March 26, 2023 |
| Submission Date | November 21, 2022 |
| Acceptance Date | March 6, 2023 |
| Published in Issue | Year 2023 |