Well-Posedness of Inverse Sturm–Liouville Problem with Fractional Derivative

Koyunbakan, Hikmet; Shah, Kamal; Abdeljawad, Thabet

doi:10.1007/s12346-022-00727-2

Cited by 21 publications

(4 citation statements)

References 34 publications

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“…Consequently, the topic of fractional differential equations is increasingly recognized and studied. For further research on fractional differential equations, refer to [1][2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Existence, uniqueness, and Ulam stability of solutions of fractional conformable Langevin system on the ethane graph

Wang,

Yuan

2024

Math Methods in App Sciences

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The present study examines the Langevin coupled boundary value problem with the fractional conformable derivative on the ethane graph. The main objective of this research is to establish the existence and uniqueness of solutions with the help of the fixed point theorem and to analyze the Ulam stability of the corresponding problem. Several examples are provided to demonstrate the obtained results.

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Section: Introductionmentioning

confidence: 99%

Existence, uniqueness, and Ulam stability of solutions of fractional conformable Langevin system on the ethane graph

Wang,

Yuan

2024

Math Methods in App Sciences

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“…By changing these parameters, the problem can be named differently, for example, if the problem is treated with eigenvalues the inverse eigenvalue problem occurs and if its with the nodal points the inverse nodal problem arises. However there are many studies on fractional Sturm-Liouville Problem (SLP) and inverse SLP as discussed in [2,4,11,16,20,23,28,30,31,34] and the inverse nodal problem can be found in [3,9,10,12,13,15,21,22,26,27], it seems that these results are not enough as such many different researches are continuously being carried out in this field. Some authors introduced a formula for the potential function in inverse nodal problem as in [3].…”

Section: Introductionmentioning

confidence: 99%

Inverse nodal problem with fractional order conformable type derivative

Sa'idu,

Koyunbakan,

Shah

et al. 2024

J. Math. Computer Sci.

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The present paper is about the inverse nodal problem for Sturm-Liouville problem with eigenparameter in the boundary condition using the conformable derivative approach. We defined a function f(µ) generally in the boundary condition and we found the zeros of the eigenfunctions (nodal points) by nucleus function K(x, t), which is a derived transformation operator. Then, we obtained the potential function by using the nodal parameters.

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“…It is possible to encounter many studies on this subject. The results given for the inverse SLP including classical derivative are given recently in case of conformable derivative [5,9,10,14,16,[30][31][32][33][34][35][36]. But results on inverse problem part have not reached the desired level yet.…”

Section: Introductionmentioning

confidence: 99%

Uniqueness of the potential in conformable Sturm‐Liouville problem

Koyunbakan

2023

Math Methods in App Sciences

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This study is about the inverse problem of the conformable Sturm‐Liouville problem SLP. Namely, we first defined the problem with separable boundary conditions and gave some of its spectral properties. Then, by spectral data, we showed that the potential and the constants in the boundary conditions are coincident for two different problems. Here, the potential is in the space . We have also shown that if the potential function has the property of being symmetrical, only one spectrum is sufficient to find this function as uniquely. It is worth remembering that the methods and calculations used here are similar to those in the SLP with classical derivative. However, we think results will be valuable in Sturm‐Liouville theory.

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Well-Posedness of Inverse Sturm–Liouville Problem with Fractional Derivative

Cited by 21 publications

References 34 publications

Existence, uniqueness, and Ulam stability of solutions of fractional conformable Langevin system on the ethane graph

Existence, uniqueness, and Ulam stability of solutions of fractional conformable Langevin system on the ethane graph

Inverse nodal problem with fractional order conformable type derivative

Uniqueness of the potential in conformable Sturm‐Liouville problem

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