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].
To the authors' best knowledge, the following works provide all results available and analyze adaptive lowest-order Courant finite elements for three particular situations: The work [56] considers the p -Laplacian, while [18,57] consider model problems in the frame of strongly-monotone operators, AFEM for eigenvalue problems is analyzed in [58 61].
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.
Recently, many authors studied the problem of finding a common element of the set of fixed points of nonexpansive or quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of an equilibrium problem in the frame work of Hilbert spaces and Banach spaces respectively; see, for instance, [11 15] and the references therein.
This problem has no solution in the frame of asexual ("homeogenomic") lineages.
