Some Further Extensions Considering Discrete Proportional Fractional Operators

Abstract

In this paper, some attempts have been devoted to investigating the dynamic features of discrete fractional calculus (DFC). To date, discrete fractional systems with complex dynamics have attracted the most consideration. By considering discrete [Formula: see text]-proportional fractional operator with nonlocal kernel, this study contributes to the major consequences of the certain novel versions of reverse Minkowski and related Hölder-type inequalities via discrete [Formula: see text]-proportional fractional sums, as presented. The proposed system has an intriguing feature not investigated in the literature so far, it is characterized by the nabla [Formula: see text] fractional sums. Novel special cases are reported with the intention of assessing the dynamics of the system, as well as to highlighting the several existing outcomes. In terms of applications, we can employ the derived consequences to investigate the existence and uniqueness of fractional difference equations underlying worth problems. Finally, the projected method is efficient in analyzing the complexity of the system.

Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

“…The heredity properties, the memory, and the crossover behavior can only be observed in a model with a fractional-order system. The fractional calculus with different fractional operators and their applications have been found, in integrodifferential equations [12] , the development in the operators [13] , [14] , application to epidemiology [15] , [16] , [17] , application to wave dynamics equations, [18] , [19] etc. The COVID-19 model with time delay and stochastic differential equation is explored in [20] .…”

Forecasting Compressive Strength of RHA Based Concrete Using Multi-Expression Programming

“…The performance indices must have values less than 0.1. For the situation of optimal moisture content, the requirement of additional external validation, namely, R m > 0.5, is met [ 63 , 64 , 65 ]. Additionally, the squared correlation coefficient ( ) between the estimated and experimental datasets, as well as the correlation coefficient ( ) between the experimental and estimated values, must approach one [ 66 , 67 , 68 ].…”

“…The validation process repeats for ten times, and at the end, the average accuracy is obtained from the ten times repetition. The generalization performance and the reliability of the model are well represented by 10 K-fold cross-validations [ 65 ]. The cross-validation tests for individual MEP model are represented in Figure 11 .…”

Assessing the potential impact of COVID-19 Omicron variant: Insight through a fractional piecewise model

“…Fractional calculus has a memory effect, which aids in correctly predicting physical systems or mathematical models. This has led to new advancements in developing new operators such as Riemann–Liouville-Caputo, Atangana-Baleanu ( ), and Caputo–Fabrizio fractional-order derivatives in integer and non-integer orders that have been proposed to be applied to solve real-world problems, for example, the applications in integrodifferential equations [23] , the new advancement and development in fractional operators [24] , [25] , application to epidemiology [26] , [27] , [28] , [29] , [30] , [31] , application to wave dynamics equations, [32] , [33] and other physical problems [34] , [35] , [36] etc. Some recent applications of fractional calculus in physical sciences has been discussed by the authors recently [37] , [38] , [39] .…”