On multiplicative conformable fractional integrals: theory and applications
BOUNDARY VALUE PROBLEMS, vol.2025, no.1, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2025 Issue: 1
- Publication Date: 2025
- Doi Number: 10.1186/s13661-025-02026-6
- Journal Name: BOUNDARY VALUE PROBLEMS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
- Kocaeli University Affiliated: No
Abstract
In this paper, we first introduce the multiplicative conformable left and right fractional integrals, followed by the derivation of key properties, such as integrability, boundedness, continuity, and the semi-group property, for the newly defined multiplicative conformable fractional integrals. Then, we establish the Hermite-Hadamard inequalities in three distinct senses for multiplicative conformable fractional integrals. Moreover, we present several corresponding midpoint and trapezoidal inequalities for the obtained Hermite-Hadamard inequalities including multiplicative conformable fractional integrals. By special cases, we present the relations between newly obtained inequalities for multiplicative conformable fractional integrals and existing results for multiplicative Riemann-Liouville fractional integrals and multiplicative integrals. Furthermore, we give some new Hermite-Hadamard type, trapezoid type and midpoint type inequalities or multiplicative Riemann-Liouville fractional integrals. Finally, we give several examples and 3D graphs to illustrate the main results.