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If the left and right derivatives have different signs (a non-differentiable point), then there are two possibilities.
Here G + ′ ( 0 ) and I + ′ ( 0 ) are the right derivatives of G at θ = 0 and of I ( t ) at t = 0, respectively.
Apart from their possible applications, equations with left and right derivatives is an interesting and new field in fractional differential equations theory.
The total variation equation is expressed in divergence form, hence also the Eq. (8.8) satisfied by the right derivatives (v_h = X^r_h u_epsilon ) is in the same form.
Moreover, formulae for the first two right derivatives D+k∥Φ t)∥p, k=1,2, are calculated and applied to determine the best upper bounds on ∥Φ t)∥p in certain classes of bounds.
By the traditional representation accepted in mathematics, mechanics and theoretical physics, the time-derivatives are defined as the right derivatives and are used in this way in differential equations describing processes in nature and technology.
Similar(46)
denotes right derivative of.
Calculating the upper right derivative along system (4.1).
Let p ( t ) be the right derivative of M ( u ).
Calculating the upper right derivative along the solution of (2.2), by condition, we have (323).
We denote the right derivative of a real-valued function f by (f_{r}').
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