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Comparison principles for fractional differential equations with the Caputo derivatives
Advances in Difference Equations, 2018 In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n ...
Ziqiang Lu, Yuanguo Zhu
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On applications of Caputo k-fractional derivatives [PDF]
Advances in Difference Equations, 2019 This research explores Caputo k-fractional integral inequalities for functions whose nth order derivatives are absolutely continuous and possess Grüss type variable bounds. Using Chebyshev inequality (Waheed et al. in IEEE Access 7:32137–32145, 2019) for
Ghulam Farid +5 more
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Hermite–Jensen–Mercer Type Inequalities for Caputo Fractional Derivatives
Journal of Function Spaces, 2020 In this article, certain Hermite–Jensen–Mercer type inequalities are proved via Caputo fractional derivatives. We established some new inequalities involving Caputo fractional derivatives, such as Hermite–Jensen–Mercer type inequalities, for ...
Jinchao Zhao +4 more
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The mathematical description of the bulk fluid flow and that of the content impurity dispersion, obtained by replacing integer order temporal derivatives with general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, are objective [PDF]
INCAS Bulletin, 2021 In the field of fractional calculus applications, there is a tendency to admit that “integer-order derivatives cannot simply be replaced by fractional-order derivatives to develop fractional-order theories”.
Agneta M. BALINT, Stefan BALINT
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Mathematics, 2022 The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics ...
Ravi Agarwal +2 more
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A new Definition of Fractional Derivative and Fractional Integral [PDF]
Kirkuk Journal of Science, 2018 In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
Ahmed M. Kareem
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Fractal and Fractional, 2023 In this paper, a delayed reaction-diffusion neural network model of fractional order and with several constant delays is considered. Generalized proportional Caputo fractional derivatives with respect to the time variable are applied, and this type of ...
Ravi P. Agarwal +2 more
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Complexity, 2021 The Caputo conformable derivative is a new Caputo-type fractional differential operator generated by conformable derivatives. In this paper, using Banach fixed point theorem, we obtain the uniqueness of the solution of nonlinear and linear Cauchy problem
Zhongqi Peng +3 more
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An analytical solution for the Caputo type generalized fractional evolution equation
Alexandria Engineering Journal, 2022 The Caputo type generalized fractional evolution equation is studied in this paper. Since the Caputo type generalized fractional derivative is well-known for being the generalization of Caputo fractional derivatives, this article’s studies contribute to ...
Wannika Sawangtong, Panumart Sawangtong
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Some Hermite–Jensen–Mercer type inequalities for k-Caputo-fractional derivatives and related results
Advances in Difference Equations, 2020 In this paper, certain Hermite–Hadamard–Mercer type inequalities are proved via k-Caputo fractional derivatives. We established some new k-Caputo fractional derivatives inequalities with Hermite–Hadamard–Mercer type inequalities for differentiable ...
Shupeng Zhao +5 more
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