Two New Approximations for Variable-Order Fractional Derivatives
Keyword(s):
We introduced a parameter σ(t) which was related to α(t); then two numerical schemes for variable-order Caputo fractional derivatives were derived; the second-order numerical approximation to variable-order fractional derivatives α(t)∈(0,1) and 3-α(t)-order approximation for α(t)∈(1,2) are established. For the given parameter σ(t), the error estimations of formulas were proven, which were higher than some recently derived schemes. Finally, some numerical examples with exact solutions were studied to demonstrate the theoretical analysis and verify the efficiency of the proposed methods.
2019 ◽
Vol 137
(24)
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pp. 48796
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2016 ◽
Vol 7
(2)
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pp. 271-283
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2020 ◽
Vol 134
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pp. 109695
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A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics
2017 ◽
Vol 77
(1)
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pp. 375-383
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2016 ◽
Vol 26
(3)
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pp. 429-435
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2015 ◽
Vol 293
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pp. 184-200
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