We introduce a new local derivative that generalizes the so-called alternative "fractional" derivative recently proposed. We denote this new differential operator by DMα,β, where the parameter α, associat...
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In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly conv...
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We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski’s inequality. We show two new theorems associated with this inequality, as well...
In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the ψ-Hilfer fract...
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Using Gronwall inequality we will investigate the Ulam-Hyers and generalized Ulam-Hyers-Rassias stabilities for the solution of a fractional order pseudoparabolic partial differential equation.26A33, 35R11, 35B35, 35K...
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We introduce a new derivative, the so-called truncated V-fractional derivative for α-differentiable functions through the six parameters truncated Mittag-Leffler function, which generalizes different fractional deriv...
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The introduction of a fractional differential operator defined in terms of the Riemann-Liouville derivative makes it possible to generalize the kinetic equations used to model relaxation in dielectrics. In this contex...
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The consideration of cooperative networked systems has raised fundamental new questions and challenges. We consider networked systems from various domains including control, communications, sensing, sociology, economi...
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The consideration of cooperative networked systems has raised fundamental new questions and challenges. We consider networked systems from various domains including control, communications, sensing, sociology, economics and biology. We first describe a general model for modeling such systems that involves several interacting dynamic multigraphs. These multigraphs evolve in at least three planes. At the higher plane (layer) we have the network of cognitive agents, where decisions are made and executed. At the intermediate plane (layer) we have the information network, where data, models, observations and signalling are represented. At the lower plane (layer) we have the communication network that supports the information and agent networks. There are several ways to capture these ideas and principles, and the one presented here is one of the simpler possible representations. The lower layer is more connected to the physical layer, while the middle and higher layer are more logical. The networks involve have links and nodes that are annotated by weights that can be scalar, vector or even policies and rules. Furthermore the networks are dynamic. The resulting dynamic models are very complex and require a combination of methods from analysis, algebra, logic and optimization. The simplest possible model involves two interacting multigraphs: (a) the collaboration multigraph, which describes the time varying relation of collaboration between the agents; and (b) the communication multigraph, which describes the time varying communications that occur between the agents. We link these concepts to ideas from distributed computing, distributed programs and distributed computer hardware. We also link this representation to the behavior and structure models used in modern model-based-systems engineering. We describe a novel path-oriented characterization of these activities in networked dynamic systems. Next we introduce three fundamental problems and challenges emerging from thi
Using the ψ−Hilfer fractional derivative, we present a study of the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of the fractional Volterra integral-differential equation by means of fixed-point method.2...
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We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the ψ-Hilfer fractional derivative. In addition, we discuss the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of its solutions...
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