A Study on k-Generalized ψ-Hilfer Derivative Operator

A Study on k-Generalized ψ-Hilfer Derivative Operator

In this paper, we generalize the ψ -Hilfer fractional derivative and discuss some of its properties. We prove existence, uniqueness and stability results for a class of initial value problems for implicit nonlinear fractional differential equations involving generalized ψ -Hilfer fractional derivati...

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Veröffentlicht in:Vietnam journal of mathematics 2024-03, Vol.52 (1), p.25-43
Hauptverfasser: Salim, Abdelkrim, Lazreg, Jamal Eddine, Ahmad, Bashir, Benchohra, Mouffak, Nieto, Juan J.
Format: Artikel
Sprache:eng
Schlagworte:
Boundary value problems
Differential equations
Fractional calculus
Mathematics
Mathematics and Statistics
Operators (mathematics)
Original Article
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Zusammenfassung:In this paper, we generalize the ψ -Hilfer fractional derivative and discuss some of its properties. We prove existence, uniqueness and stability results for a class of initial value problems for implicit nonlinear fractional differential equations involving generalized ψ -Hilfer fractional derivative. The uniqueness result for the given problem is obtained via the Banach contraction mapping principle. In addition, two examples are given to illustrate our results.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-022-00561-8