Inverse fractional Sturm‐Liouville problem with eigenparameter in the boundary conditions

Abstract

Ambarzumyan theorem is one of the first results of the inverse spectral theory. In this work, Ambarzumyan's theorem is proved for a fractional derivative Sturm-Liouville problem. In addition, a general function that depends on the eigenvalue parameter under boundary conditions is considered.

Coincidence Theory of a Nonlinear Periodic Sturm–Liouville System and Its Applications

“…Based on this paper, we will further continue to study the dynamics of Equation (1) under pulse, delay and random effects. In addition, inspired by the papers [13][14][15][16][17][18][19][20][22][23][24][42][43][44][45][46][47][48][49][50][51][52], we will also study the Sturm-Liouville equation involving fractional differential as well as reaction-diffusion terms in the future.…”

“…The latest research trends on the S-L equation mainly include the following aspects. The first involves the theoretical and numerical methods and applications of inverse S-L problems (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]). The second focuses on the investigation of some generalized S-L equations, such as the fractional differential S-L equation (see [13][14][15][17][18][19][20][21][22][23][24]) and the S-L equation on time scales (see [25][26][27][28][29][30][31][32][33][34]).…”

“…The first involves the theoretical and numerical methods and applications of inverse S-L problems (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]). The second focuses on the investigation of some generalized S-L equations, such as the fractional differential S-L equation (see [13][14][15][17][18][19][20][21][22][23][24]) and the S-L equation on time scales (see [25][26][27][28][29][30][31][32][33][34]). The third deals with the S-L problems with certain singularity (see [35][36][37][38]) or discontinuity (see [11,12]).…”

Inverse nodal problem with fractional order conformable type derivative

“…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].…”

“…Some authors introduced a formula for the potential function in inverse nodal problem as in [3]. The authors in [31] treated the inverse eigenvalue problem of the SLP using conformable derivative approach with eigenparameter in the boundary condition and here in this work we treated the same problem under the same derivative approach and developed the inverse nodal problem.…”