Differential equations with tempered Ψ-Caputo fractional derivative
Mathematical Modelling and Analysis, 2021 In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative.
Milan Medveď, Eva Brestovanská
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Incomplete Caputo fractional derivative operators [PDF]
Advances in Difference Equations, 2018 The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hypergeometric functions and obtain their integral ...
Mehmet Ali Özarslan, Ceren Ustaoglu
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A study on the dynamics of alkali–silica chemical reaction by using Caputo fractional derivative [PDF]
Pramana, 2022 In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using the Caputo fractional derivative. We solve a non-linear fractional-order system containing six differential equations to understand the ASR ...
Kumar P +3 more
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Soret Effect on MHD Casson Fluid over an Accelerated Plate with the Help of Constant Proportional Caputo Fractional Derivative. [PDF]
ACS OmegaNon-Newtonian fluid flow is significant in engineering and biomedical applications such as thermal exchangers, electrical cooling mechanisms, nuclear reactor cooling, drug delivery, blood flow analysis, and tissue engineering.
Abbas S +6 more
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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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Nonlinear Caputo Fractional Derivative with Nonlocal Riemann-Liouville Fractional Integral Condition Via Fixed Point Theorems [PDF]
Symmetry, 2019 In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann–Liouville integral boundary value problem (BVP): c D 0 + q u ( t ) = f ( t , u ( t ) ) , t ∈ [ 0 , T ] , u ( k ) ( 0 ) = ξ k , u ( T ) = ∑ i = 1 m β i R L I 0
Piyachat Borisut +3 more
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Analytical Solutions of a Class of Fluids Models with the Caputo Fractional Derivative
Fractal and Fractional, 2022 This paper studies the analytical solutions of the fractional fluid models described by the Caputo derivative. We combine the Fourier sine and the Laplace transforms.
Ndolane Sene
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Subdiffusion equation with Caputo fractional derivative with respect to another function [PDF]
Physical Review E, 2021 We show an application of a subdiffusion equation with Caputo fractional time derivative with respect to another function g to describe subdiffusion in a medium having a structure evolving over time. In this case a continuous transition from subdiffusion
Tadeusz Kosztołowicz, Aldona Dutkiewicz
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Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations [PDF]
Numerical Mathematics: Theory, Methods and Applications, 2022 In this paper, we propose a fast second-order approximation to the variable-order (VO) Caputo fractional derivative, which is developed based on L2-1σ formula and the exponentialsum-approximation technique.
Jiali Zhang, Zhi-Wei Fang, Hai‐Wei Sun
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Generalized Laplace transform and tempered ψ-Caputo fractional derivative
Mathematical Modelling and Analysis, 2023 In this paper, images of the tempered Ψ-Hilfer fractional integral and the tempered Ψ-Caputo fractional derivative under the generalized Laplace transform are derived.
M. Medveď, M. Pospíšil
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