A Study on k -Generalized ψ -Hilfer Derivative Operator
Vietnam Journal of Mathematics(2024)
摘要
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.
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关键词
ψ-Hilfer fractional derivative,k-generalized ψ-Hilfer fractional derivative,Cauchy-type problem,Existence and uniqueness,Generalized Gronwall inequality,26A33,36A08,34A12,34A40
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