Sentence examples for order of a function from inspiring English sources

The Riemann-Liouville fractional primitive of order of a function is given by (2.1).

The Riemann-Liouville fractional integral of order of a function is given by (2.1).

The Riemann-Liouville fractional integral operator of order, of a function is defined as (2.2).

The fractional integral of order   of a function is defined as (2.1).

The Caputo fractional derivative of order of a function, is defined as (2.1).

The Riemann-Liouville fractional primitive of order of a function of order is defined by (2.7).

The Riemann-Liouville fractional derivative of order for a function is defined by (23).

The Riemann-Liouville fractional derivative of order for a function is defined by (2.2). provided the right-hand side is pointwise defined on.

The Riemann-Liouville fractional integral of order for a function is defined as (2.2). provided the right-hand side is pointwise defined on.

The Riemann-Liouville fractional order derivative of order α of a function f ∈ L 1 ( [ 0, b ], X ) given on the interval [ 0, b ] is defined by D L α f ( t ) = 1 Γ ( n − α ) d n d t n ∫ 0 t ( t − s ) n − α − 1 f ( s ) d s, where α ∈ ( n − 1, n ], n ∈ N. Definition 2.3 ([16]).

The Caputo fractional order derivative of order α of a function f ∈ L 1 ( [ 0, b ], X ) given on the interval [ 0, b ] is defined by D α f ( t ) = 1 Γ ( 1 − α ) ∫ 0 t ( t − s ) − α f ( 1 ) ( s ) d s.