Sentence examples for problems in the frame of from inspiring English sources

We can unify such existence and stability problems in the frame of dynamic equations on time scales.

We proved existence and uniqueness theorems by means of the Banach fixed point theorem for initial value problems in the frame of (ABC) and (ABR) derivatives.

In Section 4, we prove, using the Banach fixed point theorem, some existence and uniqueness theorems for Riemann ((ABR)) and Caputo ((ABC)) type initial value problems in the frame of fractional operators with Mittag-Leffler kernels, supported by some examples.

To set up the basic concepts we proved existence and uniqueness theorems by means of the Banach fixed point theorem for initial value problems in the frame of CFC and CFR derivatives.

In this work we extend the fractional calculus with exponential kernels proposed and studied in [8, 9] to higher order, prove some existence and uniqueness theorems and prove Lypanouv type inequalities for boundary value problems in the frame of this calculus.

The extension for right fractional operators and integrals is also considered to be used later by researchers in solving higher order fractional variational problems in the frame of Mittag-Leffler kernels by means of integration by parts depending on left and right fractional operators [12 14].

In this section, we will consider the following discrete spectral problem in the frame of the AKNS system: E φ n = U n ( u, λ ) φ n, U n ( u, λ ) = ( λ 2 λ u n λ v n β ), (2).

Another inherent problem in the framing of autism as a disease -- which, in medicine, means a particular abnormal, pathological condition that affects part or all of an organism, compared to a statistical sense of normality.

Yet the problems lie in the framing of policy frameworks, not in the technologies themselves.

Then we prove a Lyapunov type inequality for the Riemann type fractional boundary value problems

This problem has no solution in the frame of asexual ("homeogenomic") lineages.