Results 11 to 20 of about 2,624 (188)

Anomalous Relaxation in Dielectrics with Hilfer Fractional Derivative [PDF]

Journal of Applied Nonlinear Dynamics, 2021
Summary: We introduce a new relaxation function depending on an arbitrary parameter as a solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami regarding, anomalous relaxation in dielectrics, which are recovered as particular cases.
Gómez Plata, A. R., Capelas de Oliveira, E., Rosa, Ester C. A. F.   +2 more
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Maximum Principle for Nonlinear Fractional Differential Equations with the Hilfer Derivative

Fractal and Fractional, 2023
In this paper, two significant inequalities for the Hilfer fractional derivative of a function in the space ACγ([0,b],Rn), 0≤γ≤1 are obtained. We first verified the extremum principle for the Hilfer fractional derivative.
Abu Bakr Elbukhari, Zhenbin Fan, Gang Li
doaj   +1 more source

Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient

Fractal and Fractional, 2021
The aim of this paper is to establish the existence and uniqueness results for differential equations of Hilfer-type fractional order with variable coefficient.
Fang Li, Chenglong Wang, Huiwen Wang
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Reachability of fractional dynamical systems using ψ-Hilfer pseudo-fractional derivative [PDF]

Journal of Mathematical Physics, 2021
In this paper, we investigate the reachability of linear and non-linear systems in the sense of the ψ-Hilfer pseudo-fractional derivative in g-calculus by means of the Mittag–Leffler functions (one and two parameters). In this sense, two numerical examples are discussed in order to elucidate the investigated results.
J. Vanterler da C. Sousa, M. Vellappandi, V. Govindaraj, Gastão S. F. Frederico   +3 more
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Infinite Interval Problems for Fractional Evolution Equations

Mathematics, 2022
In this paper, we investigate infinite interval problems for the fractional evolution equations with Hilfer fractional derivative. By using the generalized Ascoli–Arzelà theorem and some new techniques, we prove the existence of mild solutions of Hilfer ...
Yong Zhou
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$q$-ANALOGUE OF HILFER-KATUGAMPOLA FRACTIONAL DERIVATIVES AND APPLICATIONS

South East Asian Journal of Mathematics and Mathematical Sciences, 2023
Anovel qp-variant of the q−Mittag-Leffler functionandaquantum analoguepDα,β a±,qoftheHilfer-Katugampolafractionalderivativearedefined.Then, generalizationsoftheq−Taylor’sformulaandtheq−differentialtransformandits inverseareobtainedusingtheoperator pDα,β a±,q. Additionally, afewpropertiesof thenewlydefinedq-differential transformareestablished. Finally,
Mallah, Ishfaq Ahmad, Chanchlani, Lata, Alha, Subhash   +2 more
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A Survey on Recent Results on Lyapunov-Type Inequalities for Fractional Differential Equations

Fractal and Fractional, 2022
This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety of fractional derivative operators and boundary conditions.
Sotiris K. Ntouyas, Bashir Ahmad, Jessada Tariboon   +2 more
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Euler–Lagrange equations for variational problems involving the Riesz–Hilfer fractional derivative

Journal of Taibah University for Science, 2020
In this paper, we obtain the Euler-Lagrange equations for different kind of variational problems with the Lagrangian function containing the Riesz-Hilfer fractional derivative.
A. G. Ibrahim, A. A. Elmandouh
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Null Controllability of Hilfer Fractional Stochastic Differential Inclusions

Fractal and Fractional, 2022
This paper gives the null controllability for nonlocal stochastic differential inclusion with the Hilfer fractional derivative and Clarke subdifferential.
Hamdy M. Ahmed, Mahmoud M. El-Borai, Wagdy El-Sayed, Alaa Elbadrawi   +3 more
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On a Differential Equation Involving Hilfer‐Hadamard Fractional Derivative [PDF]

Abstract and Applied Analysis, 2012
This paper studies a fractional differential inequality involving a new fractional derivative (Hilfer‐Hadamard type) with a polynomial source term. We obtain an exponent for which there does not exist any global solution for the problem. We also provide an example to show the existence of solutions in a wider space for some exponents.
Qassim, M. D., Furati, K. M., Tatar, N.-E.   +2 more
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