Results 231 to 240 of about 8,551 (258)

Fractional integral inequalities and their applications to fractional differential equations

Acta Mathematica Scientia, 2016
Abstract In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.
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Integration of Fractional Differential Equations without Fractional Derivatives

2021 9th International Conference on Systems and Control (ICSC), 2021
Nezha Maamri, Jean-Claude Trigeassou
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Fractional integral problems for Hadamard–Caputo fractional Langevin differential inclusions

Journal of Applied Mathematics and Computing, 2015
The authors consider the differential inclusion (of fractional type) \[ D^{\alpha}\big(D^{\beta}+\lambda\big)x(t)\in F\big(t,x(t)\big) \] for \(t\in[1,e]\). The differential inclusion is subjected to the conditions (of nonlocal type) \[ \sum_{i=1}^{m}\theta_{i}I^{\mu_i}x\left(\eta_i\right)=\sum_{j=1}^{n}\phi_{j}I^{\gamma_j}x\left(\omega_j\right) \] and
Ntouyas, Sotiris K., Tariboon, Jessada
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Differentiability of Fractional Integrals Whose Kernels Contain Fractional Brownian Motions

Ukrainian Mathematical Journal, 2001
The authors find conditions upon a function \(\beta\) under which the fractional integral \[ \Phi (t)=\int_0^t\varphi (t,s) ds, \] where \[ \varphi (t,s)=(t-s)^{1/2-H_0}\beta (s/t)\int_0^s\alpha (u) dB_u^H,\quad 1 ...
Krvavych, Yu. V., Mishura, Yu. S.
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On physical interpretations of fractional integration and differentiation

Theoretical and Mathematical Physics, 1995
The paper deals with physical interpretation of fractional integration and differentiation in the Riemann-Liouville form [see Sections 2 and 6 in the book by \textit{S. G. Samko}, \textit{A. A. Kilbas} and \textit{O. I. Marichev}: ``Fractional integrals and derivatives: Theory and applications'' (Russian, 1987; Zbl 0617.26004; English translation, 1993;
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Fractional Differential and Integral Inequalities with Applications

2016
Abstract : The monotone method extended to such systems is called the generalized monotone method. Here the generalized monotone method has been extended to the Caputo fractional differential equation of order q (where 0q1) withan initial condition as well as the existence of coupled minimal and maximal solutions for such an equation and a numerical ...
A. S. Vatsala, Donna Stutson
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Fractional Integration and Differentiation of Asymptotic Relations and Applications

Mathematical Methods in the Applied Sciences
ABSTRACTThe main results of this paper show how asymptotic relations are preserved when integrated or differentiated in the sense of fractional operators. In some of them, the concept of regular variation plays a role. We derive a fractional extension of the Karamata integration theorem and of the monotone density theorem, among others.
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Discretization of Fractional-Order Differentiators and Integrators

IFAC Proceedings Volumes, 2014
Abstract This paper introduces a closed form discretization method of fractional-order differentiators or integrators. Unlike the continued fraction expansion technique, or the infinite impulse response of second-order IIR-type filters, the proposed technique generalizes the Tustin operator to derive a stable and minimum 1 st and 2 nd -order ...
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Fractional Differential and Integral Operators

2022
Abdon Atangana, Seda İgret Araz
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Fractional Integration and Fractional Differentiation of the M-Series

2010
In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving ...
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