Results 301 to 310 of about 191,994 (333)

On the fractional differential equations

Applied Mathematics and Computation, 1992
The author deals with the semilinear differential equation \(d^ \alpha x(t)/dt^ \alpha=f(t,x(t))\), \(t>0\), where \(\alpha\) is any positive real number. In [Kyungpook Math. J. 28, No. 2, 119-122 (1988; Zbl 0709.34011)] the author has proved the existence, uniqueness, and some properties of the solution of this equation when ...
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Fractional Differential Equations

2018
Let the fractional differential equation (FDE) be $$\displaystyle (D^\alpha _{a_+}y)(t) = f[t,y(t)],\hspace {0.2 cm} \alpha > 0,\hspace {0.2 cm} t > a,$$ with the conditions: $$\displaystyle (D^{\alpha - k}_{a+}y)(a+) = b_k,\hspace {0.2 cm} k = 1,\ldots , n,$$ called also Riemann–Liouville FDE.
Constantin Milici, Gheorghe Drăgănescu, J. A. Tenreiro Machado   +2 more
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Fractional Differential Equations in Electrochemistry

Civil-Comp Proceedings, 2009
Electrochemistry was one of the first sciences to benefit from the fractional calculus. Electrodes may be thought of as ''transducers'' of chemical fluxes into electricity. In a typical electrochemical cell, chemical species, such as ions or dissolved molecules, move towards the electrodes by diffusion.
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On the fractional differential equations with uncertainty

Nonlinear Analysis: Theory, Methods & Applications, 2011
Abstract This paper is based on the concept of fuzzy differential equations of fractional order introduced by Agarwal et al. [R.P. Agarwal, V. Lakshmikantham, J.J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal. 72 (2010) 2859–2862].
Vasile Lupulescu, Sadia Arshad
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Optimization of a Fractional Differential Equation [PDF]

, 2018
We consider a linear quadratic optimization problem where the state is governed by a fractional ordinary differential equation. We also consider control constraints. We show existence and uniqueness of an optimal state–control pair and propose a method to approximate it.
Abner J. Salgado, Enrique Otárola
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Fuzzy Fractional Differential Equations [PDF]

, 2020
Different materials and processes in many applied sciences like electrical circuits, biology, biomechanics, electrochemistry, electromagnetic processes and, others are widely recognized to be well predicted by using fractional differential operators in accordance with their memory and hereditary properties.
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WAVE EQUATION AND FRACTIONAL DIFFERENTIATION

2023
Source: Masters Abstracts International, Volume: 12-02, page: 1330.
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Fractional Ordinary Differential Equations

2020
First we consider simple fractional ordinary differential equations: $$\displaystyle \begin{aligned} D_t^{\alpha} u(t) = -\lambda u(t) + f(t), \quad ...
Katarzyna Ryszewska, Adam Kubica, Masahiro Yamamoto   +2 more
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Generalized Fractional Differential Equations

2019
In this chapter, the theory of linear and nonlinear fractional differential equations is developed and extended to a large class of generalized fractional evolutions. The used method is mostly that of semigroups and propagators as developed in Chapters 4 and 5. As previously, general facts are illustrated on concrete examples.
Vassili N. Kolokoltsov, Vassili N. Kolokoltsov   +1 more
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Fractional Integro-Differential Equations

2018
Fractional calculus is a generalization of the classical differentiation and integration of non-integer order. Fractional calculus is as old as differential calculus.
Toka Diagana, Toka Diagana, Toka Diagana
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