A new kind of uniqueness theorems for inverse Sturm-Liouville problems

Abstract

We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyan's theorem.

Fractional Coupled Hybrid Sturm–Liouville Differential Equation with Multi-Point Boundary Coupled Hybrid Condition

“…During the history of mathematics, an important framework of problems called Sturm-Liouville differential equations has been in the spotlight of the mathematicians of applied mathematics and engineering; scientists of physics, quantum mechanics, and classical mechanics; and certain phenomena; for some examples see in [18,19] and the list of references of these papers. In such a manner, it is important that mathematicians design complicated and more general abstract mathematical models of procedures in the format of applicable fractional Sturm-Liouville differential equations, see in [20][21][22].…”

On a fractional hybrid version of the Sturm–Liouville equation

“…The Sturm-Liouville differential equation is an important differential equation in physics, applied mathematics, and other fields of engineering and science, and it has wide applications in quantum mechanics, classical mechanics, and wave phenomena (see, for example, [2] and [3] and the references therein). The existence of solutions and other properties for Sturm-Liouville boundary value problems have received considerable attention from many researchers during the last two decades (see, for example, [4][5][6][7][8][9][10][11][12][13][14][15][16][17]). Finally, a hybrid version of differential equations has a special appeal to everybody.…”

Fractional hybrid inclusion version of the Sturm–Liouville equation

“…Some differential equations such as that of Sturm-Liouville have established important relations between physics, mathematics, and other fields of engineering (see [1,2]). During the last decades, many researchers have been studying some well-known problems involving differential equations such as Sturm-Lioville boundary value problems from different views (see, for example, [3][4][5][6][7][8][9][10][11][12][13][14][15][16]). It is important that researchers try to investigate distinct versions of famous and applicable differential equations (see, for example, [17][18][19][20]).…”