The Cotangent Derivative with Respect to Another Function: Theory, Methods and Applications
Fractal and FractionalThis paper introduces a generalization of the Riemann–Liouville and Caputo cotangent derivatives and their corresponding integrals, known as the Riemann–Liouville and Caputo cotangent derivatives with respect to another function (RAF).
Lakhlifa Sadek, Ali Algefary
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Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side
Mathematical Modelling and Analysis, 2015 In this paper we deal with the problem of asymptotic integration of a class of fractional differential equations of the Caputo type. The left-hand side of such type of equation is the Caputo derivative of the fractional order r ∈ (n − 1, n) of the ...
Milan Medved, Michal Pospisil
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Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives. [PDF]
Sci Rep, 2022 Sheikh NA +3 more
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On Riemann-Liouville and Caputo Derivatives [PDF]
, 2011 Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann-Liouville (
Changpin Li, Deliang Qian, YangQuan Chen
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Several new integral inequalities via caputo fractional integral operators
, 2023 In this paper, we establish several new integral inequalities including Caputo fractional derivatives for quasi-convex, s-Godunova-Levin convex.
Butt, Saad Ihsan +2 more
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Author Correction: Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives. [PDF]
Sci Rep, 2022 Sheikh NA +3 more
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The Effect of the Caputo Fractional Derivative on Polynomiography
Mathematics Interdisciplinary Research, 2023 This paper presents the visualization process of finding the roots of a complex polynomial - which is called polynomiography - by the Caputo fractional derivative. In this work, we substitute the variable-order Caputo fractional derivative for classic derivative in Newton's iterative method. To investigate the proposed root-finding method,
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New Results on Fractional Power Series: Theory and Applications
Entropy, 2013 In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives.
Ahmad El-Ajou +3 more
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Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives
Fractal and Fractional, 2019 This paper proposes novel analytical solutions of the mass-spring-damper systems described by certain generalized fractional derivatives. The Liouville−Caputo left generalized fractional derivative and the left generalized fractional derivative ...
Ndolane Sene +1 more
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Fractional Euler-Lagrange differential equations via Caputo derivatives [PDF]
, 2010 We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler–Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given.
Malinowska,Agnieszka +2 more
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