Analysis of fractal fractional differential equations
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In this paper, the authors consider an advection-dispersion model, where the velocity is considered to be 1 and the kernels are power law, exponential decay law and the generalized Mittag-Leffler kernel.Abstract:
Nonlocal differential and integral operators with fractional order and fractal dimension have been recently introduced and appear to be powerful mathematical tools to model complex real world problems that could not be modeled with classical and nonlocal differential and integral operators with single order. To stress further possible application of such operators, we consider in this work an advection-dispersion model, where the velocity is considered to be 1. We consider three cases of the models, when the kernels are power law, exponential decay law and the generalized Mittag-Leffler kernel. For each case, we present a detailed analysis including, numerical solution, stability analysis and error analysis. We present some numerical simulation.read more
Citations
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Diverse exact solutions for modified nonlinear Schrödinger equation with conformable fractional derivative
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A new and general fractional Lagrangian approach: A capacitor microphone case study
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References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
A new Definition of Fractional Derivative without Singular Kernel
Michele Caputo,Mauro Fabrizio +1 more
TL;DR: In this article, the authors present a new definition of fractional derivative with a smooth kernel, which takes on two different representations for the temporal and spatial variable, for which it is more convenient to work with the Fourier transform.
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Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system
TL;DR: In this paper, new operators of differentiation have been introduced, such as convolution of power law, exponential decay law, and generalized Mittag-Leffler law with fractal derivative, referred as fractal-fractional differential and integral operators.
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