Results 11 to 20 of about 1,341,149 (142)
Generalized Taylor formulas involving generalized fractional derivatives
, 2017 In this paper, we establish a generalized Taylor expansion of a given function $f$ in the form $\displaystyle{f(x) = \sum_{j=0}^m c_j^{\alpha,\rho}\left(x^\rho-a^\rho\right)^{j\alpha} + e_m(x)}$ \noindent with $m\in \mathbb{N}$, $c_j^{\alpha,\rho}\in
Benjemaa, Mondher
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, 2017 In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results
Garra, Roberto +2 more
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Mathematical Problems in Engineering, 2021 In this work, through using the Caputo–Hadamard fractional derivative operator with three nonlocal Hadamard fractional integral boundary conditions, a new type of the fractional-order Sturm–Liouville and Langevin problem is introduced.
A. Salem +3 more
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A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus
, 2017 We present a new approach based on linear integro-differential operators with logarithmic kernel related to the Hadamard fractional calculus in order to generalize, by a parameter $\nu \in (0,1]$, the logarithmic creep law known in rheology as Lomnitz ...
Garra, Roberto +2 more
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Journal of Inequalities and Applications, 2021 In this work, we establish Lyapunov-type inequalities for the fractional boundary value problems with Caputo–Hadamard fractional derivative subject to multipoint and integral boundary conditions. As far as we know, there is no literature that has studied
Youyu Wang, Yuhan Wu, Zhengzi Cao
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The fractional Dodson diffusion equation: a new approach
, 2018 In this paper, after a brief review of the general theory concerning regularized derivatives and integrals of a function with respect to another function, we provide a peculiar fractional generalization of the $(1+1)$-dimensional Dodson's diffusion ...
Garra, Roberto +2 more
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Journal of Inequalities and Applications, 2022 In this study, some new Lyapunov-type inequalities are presented for Caputo-Hadamard fractional Langevin-type equations of the forms Da+βHC(HCDa+α+p(t))x(t)+q(t)x(t)=0 ...
Wei Zhang, Jifeng Zhang, J. Ni
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, 2019 This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative.
Cai, Ruiyang +3 more
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Error estimates of a high order numerical method for solving linear fractional differential equations [PDF]
, 2016 In this paper, we first introduce an alternative proof of the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound quadrature formula was used to approximate ...
Adolfsson +39 more
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Mathematical Methods in the Applied Sciences, Volume 49, Issue 2, Page 521-530, 30 January 2026.ABSTRACT This paper investigates the generalized Hyers–Ulam stability of the Laplace equation subject to Neumann boundary conditions in the upper half‐space. Traditionally, Hyers–Ulam stability problems for differential equations are analyzed by examining the system's error, particularly in relation to a forcing term.
Dongseung Kang +2 more
wiley +1 more source