The ψ-Hilfer fractional calculus of variable order and its applications

被引：0
|
作者：
Sousa, J. Vanterler da C. [1 ]
Machado, J. A. Tenreiro [2 ]
de Oliveira, E. Capelas [1 ]
机构：
[1] Imecc Unicamp, Dept Appl Math, BR-13083859 Campinas, SP, Brazil
[2] Polytech Porto, Inst Engn, Dept Elect Engn, Porto, Portugal
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2020年 / 39卷 / 04期
关键词：
Fractional calculus; psi-Hilfer fractional derivative of variable order; Approximation methods; Stability; VARIATIONAL-PROBLEMS; DIFFERENTIAL-EQUATIONS; DERIVATIVES; STABILITY; SYSTEM;
D O I：
10.1007/s40314-020-01347-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present the psi-Hilfer fractional derivatives of variable order (FDVO) of 3 types I, II and III, versions A and B, as well as their combinations. In addition, we propose approximations and relations between both derivatives, i.e., psi-Hilfer FDVO and psi-Caputo FDVO. With regard to the psi-Hilfer FDVO type II, we discuss the stability of the FVO nonlinear systems 7 solutions by means of one-parameter Mittag-Leffler functions of variable order. Examples 8 involving the FDVO Lu and Chen systems are also presented.
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页数：35
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