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An operational calculus formulation of fractional calculus with general analytic kernels
Electronic Research Archive, 2022 Fractional calculus with analytic kernels provides a general setting of integral and derivative operators that can be connected to Riemann–Liouville fractional calculus via convergent infinite series.
Noosheza Rani , Arran Fernandez
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Fractional calculus in the sky
, 2021 Fractional calculus was born in 1695 on September 30 due to a very deep question raised in a letter of L’Hospital to Leibniz. The prophetical answer of Leibniz to that deep question encapsulated a huge inspiration for all generations of scientists and is
D. Baleanu, R. Agarwal
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Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications [PDF]
Mathematics, 2021 In this paper, we first discuss the convolution series that are generated by Sonine kernels from a class of functions continuous on a real positive semi-axis that have an integrable singularity of power function type at point zero.
Yuri Luchko
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Fractional calculus, zeta functions and Shannon entropy
, 2021 This paper deals with the fractional calculus of zeta functions. In particular, the study is focused on the Hurwitz ζ \zeta function. All the results are based on the complex generalization of the Grünwald-Letnikov fractional derivative.
E. Guariglia
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Fractal and Fractional, 2022 In this study, the variable order fractional calculus of the hidden variable fractal interpolation function is explored. It extends the constant order fractional calculus to the case of variable order. The Riemann–Liouville and the Weyl–Marchaud variable
Valarmathi Raja, Arulprakash Gowrisankar
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Fractional-calculus diffusion equation [PDF]
Nonlinear Biomedical Physics, 2010 Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems.The canonical quantization of a system represented classically by one-dimensional Fick's law, and the ...
Hussam Alrabaiah, Abdul-Wali Ajlouni
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Some trapezoid and midpoint type inequalities via fractional ( p , q ) $(p,q)$ -calculus
Advances in Difference Equations, 2021 Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q ...
Pheak Neang +4 more
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Foundations of generalized Prabhakar-Hilfer fractional calculus with applications
Cubo, 2021 Here we introduce the generalized Prabhakar fractional calculus and we also combine it with the generalized Hilfer calculus. We prove that the generalized left and right side Prabhakar fractional integrals preserve continuity and we find tight upper ...
George A. Anastassiou
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Research on Rock Creep Characteristics Based on the Fractional Calculus Meshless Method
Advances in Civil Engineering, 2018 The application of fractional calculus in the rheological problems has been widely accepted. In this study, the constitutive relationship of the generalized Kelvin model based on fractional calculus was studied, and the meshless method was introduced so ...
Gang Peng, Zhanqing Chen, Jiarui Chen
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A Compact Introduction to Fractional Calculus [PDF]
arXiv, 2022 A Compact Introduction to Fractional Calculus is presented including basic definitions, fractional differential equations and special functions.
arxiv