On the fundamental solutions of a discontinuous fractional boundary value problem

Yakar, Ali; Akdoğan, Z.

doi:10.1186/s13662-017-1433-6

Cited by 14 publications

(2 citation statements)

References 18 publications

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“…Further results relating to the spectral theory of differential equations are given in [3][4][5]. Various methods have also been developed to solve various types of Sturm-Liouville problems (see, for example, [2][3][4][5][6][7][8] and references cited therein)…”

Section: Introductionmentioning

confidence: 99%

Non-classical periodic boundary value problems with impulsive conditions

ÖZTÜRK

Mukhtarov

Aydemir

2023

Journal of New Results in Science

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This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end, and two additional interaction conditions are imposed on this common end (such interaction conditions are called various names, including transmission conditions, jump conditions, interface conditions, impulsive conditions, etc.). At first, we proved that all eigenvalues are real and there is a corresponding real-valued eigenfunction for each eigenvalue. Then we showed that two eigenfunctions corresponding to different eigenvalues are orthogonal. We also defined some left and right-hand solutions, in terms of which we constructed a new transfer characteristic function. Finally, we have defined asymptotic formulas for the transfer characteristic functions and also for the eigenvalues. The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

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Section: Introductionmentioning

confidence: 99%

Non-classical periodic boundary value problems with impulsive conditions

ÖZTÜRK

Mukhtarov

Aydemir

2023

Journal of New Results in Science

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“…In 2014, Mubeen and Rehman [3] generalized the classical factorial function called -factorials as (1.9)…”

Section: Introductionmentioning

confidence: 99%

New Generalized Hypergeometric Functions

KABARA

2022

Ikonion Journal of Mathematics

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The classical Gauss hypergeometric function and the Kumar confluent hypergeometric function are defined using a classical Pochammer symbol , and a factorial function. This research paper will present a two-parameter Pochhammer symbol, and discuss some of its properties such as recursive formulae and integral representation. In addition, the generalized Gauss and Kumar confluent hypergeometric functions are defined using a two-parameter Pochhammer symbol and two-parameter factorial function and some of the properties of the new generalized hypergeometric functions were also discussed.

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Asymptotic Behavior for Eigenvalues of the Singular Sturm-Liouville Problem with Transmission Conditions

2020

Differ Equ Dyn Syst

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On the fundamental solutions of a discontinuous fractional boundary value problem

Cited by 14 publications

References 18 publications

Non-classical periodic boundary value problems with impulsive conditions

Non-classical periodic boundary value problems with impulsive conditions

New Generalized Hypergeometric Functions

Asymptotic Behavior for Eigenvalues of the Singular Sturm-Liouville Problem with Transmission Conditions

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