Numerical algorithm for the variable-order Caputo fractional functional differential equation

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A novel Jacobi operational matrix for numerical solution of multi-term variable-order fractional differential equations (2020, background): “Moreover, the fractional variable-order calculus is considered as a regular filter to supply an influential mathematical building for the description of the dynamical problems in the complex form [28,29].”
A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications (2019, background): “In addition, the operator 0 D α(t) t satisfies the following property (1<α(t)<2) [12]”
Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials (2019, background): “, tn]T , (15) then the vector ψ(t) can be expressed as follows ψ(t) = A λ(t), (16)”
Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems (2016, methodology): “Variable-order FD of Caputo type in term of the singular power-law kernel is given by [15,16]:”