The global sliding mode tracking control for a class of variable order fractional differential systems

Jiang, Jingfei; Chen, Huatao; Cao, Dengqing; Guirao, Juan Luis García

doi:10.1016/j.chaos.2021.111674

Cited by 17 publications

(2 citation statements)

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“…Subsequently, Lorenzo et al [3] and Coimbra [4] studied VO calculus by discussing its possible applications in mechanics, which marked the starting point for applications of VO operators to the analysis of different complex physical problems. After that VO fractional differential equations are widely employed in mechanics and dynamics, viscoelasticity, the modelling of transport processes, control theory because VO fractional operators can describe accurately the memory and hereditary properties of many physical phenomena and processes depending on their nonstationary power-law kernel [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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The Existence of Solution to Fractional Boundary Value Problem with Riemann-Liouville Type History-State-Based Variable-Order Derivative

Zhang

Wang

2022

Contemporary Mathematics

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The paper is devoted to studying the solutions of boundary value problem for nonlinear fractional differential equation with Riemann-Liouville type history-state-based variable-order derivative. Using Schauder fixed point theorem and Banach fixed point thoerem, we prove the existence and uniqueness of solutions in the Hölder space. Lastly, two examples are given to show the applicability of the existence theorems.

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Section: Introductionmentioning

confidence: 99%

“…(5) (6) where 1 < q(t) < 2 is a piecewise constant function, f : (0, T ] × R → R is a continuous function and D 0+ q(t) is the Riemann-Liouville type VO fractional derivative defined by…”

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confidence: 99%