Document Type
Article
Source of Publication
Partial Differential Equations in Applied Mathematics
Publication Date
9-1-2024
Abstract
In this paper, a novel general definition for the fractional derivative and fractional integral based on an undefined kernel function is introduced. For 0<α≤1, this definition aligns with classical interpretations and is applicable for calculating the derivative in an open negative interval I⊆[a,+∞),a∈R. Additionally, when α=1, the definition coincides with the classical derivative. Fundamental properties of the fractional integral and derivative, including the product rule, quotient rule, chain rule, Rolle's theorem, and the mean value theorem, are derived. These properties are illustrated through various applications to demonstrate their applicability. Furthermore, some applications of solving fractional nonlinear systems of integro-differential equations using framelets are presented.
DOI Link
ISSN
Publisher
Elsevier BV
Volume
11
Disciplines
Mathematics
Keywords
Fractional calculus, Fractional integral, Framelets, Mathematical analysis, Numerical analysis, Wavelet frames
Scopus ID
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Mohammad, Mutaz and Saadaoui, Mohamed, "A new fractional derivative extending classical concepts: Theory and applications" (2024). All Works. 6785.
https://zuscholars.zu.ac.ae/works/6785
Indexed in Scopus
yes
Open Access
yes
Open Access Type
Gold: This publication is openly available in an open access journal/series