Some fundamental fractional differential inequalities which are utilized to prove the existence of extremal solutions are also established.
The following is the Krasnoselskii's fixed point theorem which will be utilized to obtain the existence of solutions in the next section.
Moreover the results obtained are utilized to study the existence of solutions to fractional parabolic equations as an illustrative example to show the practical usefulness of the analytical results.
Secondary ion mass spectroscopy (SIMS; ION-TOF TOF.SIMS 5, Münster, Germany) was utilized to determine the existence of Ti, O, C, and Si ions, as a function of depth below the film surface.
and illustrate how our methodology can be utilized to prove the existence of oscillatory solutions for some range of the parameter p. In this case, as in [7], one may choose the function σ ( t ) = { t − 1, t ∈ [ 3 n, 3 n + 1 ], 3 n, t ∈ [ 3 n + 1, 3 n + 2.6 ], 5 t − ( 12 n + 13 ), t ∈ [ 3 n + 2.6, 3 n + 3 ].
In this section, the modified JPDA is enhanced by incorporating the probability of target existence as a track quality measure for track management, which utilizes the probability of target existence to confirm or terminate tracks, and is termed as modified joint integrated probabilistic data association (MJIPDA).
ITS also utilizes the probability of target existence as a track quality measure.
The genomes of many freshwater cyanobacteria do not contain orthologues of this 8VR although they utilize 8E Chl, indicating the existence of a second 8VR (termed BciB) unrelated to the BciA first identified in A. thaliana.
Hannah et al (2012) have noted an absence of institutionalization of PS activities, but apparently utilized as an indicator the existence of standardized procedures and structured surveillance programs as are very common in public health surveillance systems.
Our next two results utilize Theorem 2.2 to establish the existence of solutions of (1.3).
