These operators are employed in many applications, for example, combinatorics, orthogonal polynomials, basic hypergeometric functions, hypergeometric series, complex analysis, the calculus of variations, the theory of relativity, quantum mechanics, and particle physics [1 9].
Below, we give some fundamental definitions, lemmas, and preparatory facts from functional analysis, fractional calculus theory, and measures of non-compactness which will be employed in the course of this manuscript.
Such are the rewards on offer that American's analysis transforms the calculus for clubs considering whether to build new stadiums.
Recently, fractional calculus analysis and fractional dynamics are hot topics [42 48].
Theoretically, it is possible to analyze the uncertain-but-bounded of a structure by using modal analysis and interval calculus.
In [15], Annaby et al. gave a rigorous analysis of the calculus associated with D q, ω.
The discrete calculus analysis allows a generalization of the Keller Box scheme to non-simplectic meshes to be constructed.
By using modal analysis and interval calculus, we investigate the method of computing upper and lower bounds of paramenters such as, natural frequencies, modal shapes, and FRFs.
The use of random and stochastic terms is more effective in this sense, compared with other tools of deterministic analysis or fractional calculus.
In [2, 10], the inverse operator was constructed and a rigorous analysis of the calculus associated with ({D}_{q,omega}) was given.
