Hilfer-Katugampola fractional derivative [PDF]
arXiv, 2017 We propose a new fractional derivative, the Hilfer-Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer-Hadamard, Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl, generalized and Caputo-type.
arxiv
A New Mixed Fractional Derivative with Applications in Computational Biology
ComputationThis study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels.
Khalid Hattaf
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Operator theoretic approach to the Caputo derivative and the fractional diffusion equations [PDF]
arXiv, 2014 The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the functional spaces where the solutions are looked for are often the spaces of the smooth functions that are too ...
arxiv
Hamilton-Jacobi equations involving a Caputo time-fractional derivative [PDF]
arXivWe prove a representation formula of intrinsic Hopf-Lax type for subsolutions to Hamilton-Jacobi equations involving a Caputo time-fractional derivative.
arxiv
High order algorithms for Fokker-Planck equation with Caputo-Fabrizio fractional derivative [PDF]
arXiv, 2018 Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures with different scales.
arxiv
Solving General Differential Equations of Fractional Orders Via Rohit Transform [PDF]
Kirkuk Journal of Scienceinspecting the attributes of derivatives and integrals of fractional orders known as fractional derivatives and integrals. In this article, a far-out complex integral transform known as the Rohit transform (RT) is put into use for working out general ...
Rohit Gupta, Rahul Gupta, Dinesh Verma
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Hamilton-Jacobi formulation of systems within Caputo's fractional derivative [PDF]
arXiv, 2007 In this paper we develop a fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives. The fractional action function is obtained and the solutions of the equations of motion are recovered. An example is studied in details.
arxiv
Transformation Property of the Caputo Fractional Differential Operator in Two Dimensional Space [PDF]
arXiv, 2013 The transformation property of the Caputo fractional derivative operator of a scalar function under rotation in two dimensional space is derived. The study of the transformation property is essential for the formulation of fractional calculus in multi-dimensional space.
arxiv
Fractional variational principles with delay within caputo derivatives
Reports on Mathematical Physics, 2010 In this paper we investigate the fractional variational principles within Caputo derivatives in the presence of delay derivatives. The corresponding Euler-Lagrange equations are obtained for the case of one dependent variable. A generalization to n dependent variables is obtained. Physical example is analyzed in detail.
Jarad, Fahd +2 more
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Fractional advection differential equation within Caputo and Caputo–Fabrizio derivatives
Advances in Mechanical Engineering, 2016 In this research, we applied the variational homotopic perturbation method and q-homotopic analysis method to find a solution of the advection partial differential equation featuring time-fractional Caputo derivative and time-fractional Caputo–Fabrizio ...
Dumitru Baleanu +2 more
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