A Matrix Mittag–Leffler Function and the Fractional Nonlinear Partial Integro-Differential Equation in ℝn

In this paper, we introduce the matrix Mittag–Leffler function, which is a generalization of the multivariate Mittag–Leffler function, in order to investigate the uniqueness of the solutions to a fractional nonlinear partial integro-differential equation in Rn with a boundary condition based on Bana...

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Veröffentlicht in:Fractal and fractional Jg. 7; H. 9; S. 651
Hauptverfasser: Li, Chenkuan, Beaudin, Joshua, Rahmoune, Azedine, Remili, Walid
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.09.2023
Schlagworte:
Babenko’s approach
Banach spaces
Banach’s contractive principle
Boundary conditions
Control theory
Differential equations
implicit integral equation
Integral equations
Laplace transforms
matrix Mittag–Leffler function
ISSN:2504-3110, 2504-3110
Online-Zugang:Volltext
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Zusammenfassung:In this paper, we introduce the matrix Mittag–Leffler function, which is a generalization of the multivariate Mittag–Leffler function, in order to investigate the uniqueness of the solutions to a fractional nonlinear partial integro-differential equation in Rn with a boundary condition based on Banach’s contractive principle and Babenko’s approach. In addition, we present an example demonstrating applications of the key results derived using a Python code that computes the approximate value of our matrix Mittag–Leffler function.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7090651