Sentence examples for differential of order from inspiring English sources

As a result, we define fuzzy Riemann-Liouville fractional differential of order β for fuzzy-valued function f as follows.

Let B ( t ) = ( B 1 ( t ), B 2 ( t ), … B m ( t ) ) be an m-dimensional Brownian motion defined on a complete probability space ( Ω, F, P ), let d α x denote the differential of order α, and let ∥ ⋅ ∥ denote the Euclidean norm in R n. Definition 1 (R-L fractional integral [10, 12]).

From the above works, we develop the theory of boundary fractional hybrid differential equations involving Caputo differential operators of order (0

From the above works, we develop the theory of fractional hybrid differential equations involving Riemann-Liouville differential operators of order 0 < q < 1.

This note is motivated by some papers treating the fractional hybrid differential equations involving Riemann-Liouville differential operators of order (0 < alpha< 1 ).

The initial value involving singular term in Riemann-Liouville fractional differential equations of order (alphain (0,1)) is much different from Caputo fractional differential equations with the same order.

In this paper, we develop the theory of fractional hybrid differential equations with linear perturbations of second type involving Riemann-Liouville differential operators of order 0 < q < 1.

Let us consider the partial differential operator of order.

Chang and Nieto [62] considered a class of fractional differential inclusions of order.

In [4 7], bounds for solutions of fractional differential inequalities of order 0 < α < 1 are obtained.

where D m is the classical differential operator of order m.