Existence of solution for a Langevin equation involving the i/i-Hilfer fractional derivative: A variational approach

被引：1

作者：

Almaghamsi, Lamya ^{[1
]}

Alghamdi, Aeshah ^{[1
]}

Ghanmi, Abdeljabbar ^{[2
]}

机构：

[1] Univ Jeddah, Fac Sci, Dept Math & Stat, Jeddah 21493, Saudi Arabia

[2] Tunis El Manar Univ, ENIT LAMSIN, BP 37,1002 Tunis Belvdre, Tunis, Tunisia

来源：

AIMS MATHEMATICS | 2025年 / 10卷 / 01期

关键词：

variational methods; fractional calculus; Langevin equation; generalized Riemann Liouville; BOUNDARY-VALUE-PROBLEMS; POSITIVE SOLUTIONS; RESPECT;

D O I：

10.3934/math.2025024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study examines the existence of a solution for a nonvariational Langevin equation that involves the i/i-Hilfer fractional derivative. More specifically, we apply the mountain pass theorem, and then an iterative approach to establish the existence of a solution for the problem.

引用

页码：534 / 550

页数：17

共 33 条

[1] A study of nonlinear Langevin equation involving two fractional orders in different intervals
Ahmad, Bashir
Nieto, Juan J.
Alsaedi, Ahmed
El-Shahed, Moustafa
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (02) : 599 - 606
[2] Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions
Ahmad, Bashir
Nieto, Juan J.
[J]. INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 2010
[3] Weak Solution for a Fractional Langevin Inclusion with the Katugampola-Caputo Fractional Derivative
Almaghamsi, Lamya
[J]. FRACTAL AND FRACTIONAL, 2023, 7 (02)
[4] A Caputo fractional derivative of a function with respect to another function
Almeida, Ricardo
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 44 : 460 - 481
[5] Variational approach for the Kirchhoff problem involving the p-Laplace operator and the ?-Hilfer derivative
Alsaedi, Ramzi
Ghanmi, Abdeljabbar
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (08) : 9286 - 9297
[6] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[7] MAX-MIN CHARACTERIZATION OF THE MOUNTAIN PASS ENERGY LEVEL FOR A CLASS OF VARIATIONAL PROBLEMS
Bellazzini, Jacopo
Visciglia, Nicola
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (09) : 3335 - 3343
[8] Existence and uniqueness for p-Laplace equations involving singular nonlinearities
Canino, Annamaria
Sciunzi, Berardino
Trombetta, Alessandro
[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 23 (02):
[9] Iterative Approximation of Positive Solutions for Fractional Boundary Value Problem on the Half-line
Chamekh, Mourad
Ghanmi, Abdeljabbar
Horrigue, Samah
[J]. FILOMAT, 2018, 32 (18) : 6177 - 6187
[10] EXISTENCE OF POSITIVE SOLUTIONS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS
Ghanmi, A.
Horrigue, S.
[J]. UKRAINIAN MATHEMATICAL JOURNAL, 2019, 71 (01) : 39 - 49

← 1 2 3 4 →