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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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MathematicsIn the literature so far, for Caputo fractional boundary value problems of order 2q when ...
Aghalaya S. Vatsala +1 more
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A fractional model of cancer-immune system with Caputo and Caputo–Fabrizio derivatives [PDF]
The European Physical Journal Plus, 2021 Recently, it is important to try to understand diseases with large mortality rates worldwide, such as infectious disease and cancer. For this reason, mathematical modeling can be used to comment on diseases that adversely affect all people. So, this paper discuss mathematical model presented for the first time that examines the interaction between ...
Uçar, Esmehan, Özdemir, Necati
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On Caputo Fractional Derivatives via Convexity [PDF]
Kragujevac Journal of Mathematics, 2020 Summary: In this paper some estimations of Caputo fractional derivatives via convexity have been presented. By using convexity of any positive integer order differentiable function some novel results are given.
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Fractional hamilton formalism within caputo’s derivative [PDF]
Czechoslovak Journal of Physics, 2006 In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained.
Baleanu, Dumitru, Agrawal, Om. P.
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A Nonlinear Implicit Fractional Equation with Caputo Derivative [PDF]
Journal of Mathematics, 2021 In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of Banach principle.
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On a discrete composition of the fractional integral and Caputo derivative [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2022 This is an accepted version of the manuscript published in Communications in Nonlinear Science and Numerical Simulations. The changes with the previous versions included some language corrections, additional numerical simulations, and new ...
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A delayed plant disease model with Caputo fractional derivatives [PDF]
Advances in Continuous and Discrete Models, 2022 AbstractWe analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington–DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams–Bashforth–Moulton
Pushpendra Kumar +4 more
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A Caputo fractional derivative-based algorithm for optimization
CoRR, 2021 We propose a novel Caputo fractional derivative-based optimization algorithm. Upon defining the Caputo fractional gradient with respect to the Cartesian coordinate, we present a generic Caputo fractional gradient descent (CFGD) method. We prove that the CFGD yields the steepest descent direction of a locally smoothed objective function.
Yeonjong Shin +2 more
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Caputo-type modification of the Hadamard fractional derivatives [PDF]
Advances in Difference Equations, 2012 Abstract Generalization of fractional differential operators was subjected to an intense debate in the last few years in order to contribute to a deep understanding of the behavior of complex systems with memory effect. In this article, a Caputo-type modification of Hadamard fractional derivatives is introduced. The properties of the modified
Fahd Jarad +2 more
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