Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
Advances in Difference Equations, 2021 In this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions ...
Samaira Naz +2 more
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Fractional Gradient Methods via ψ-Hilfer Derivative
Fractal and Fractional, 2023 Motivated by the increase in practical applications of fractional calculus, we study the classical gradient method under the perspective of the ψ-Hilfer derivative.
Nelson Vieira +2 more
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On Hilbert-Pachpatte type inequalities within ψ-Hilfer fractional generalized derivatives
AIMS Mathematics, 2023 In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided $ \psi $-Hilfer fractional derivatives with the general kernel.
Yasemin Başcı, Dumitru Baleanu
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Lyapunov-type inequalities for sequential fractional boundary value problems using Hilfer’s fractional derivative [PDF]
Journal of Inequalities and Applications, 2019 This paper is devoted to studying the Lyapunov-type inequality for sequential Hilfer fractional boundary value problems. We first provide some properties of Hilfer fractional derivative, and then establish Lyapunov-type inequalities for a sequential ...
Wei Zhang, Wenbin Liu
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Anomalous Relaxation in Dielectrics with Hilfer Fractional Derivative [PDF]
Journal of Applied Nonlinear Dynamics, 2021 Summary: We introduce a new relaxation function depending on an arbitrary parameter as a solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami regarding, anomalous relaxation in dielectrics, which are recovered as particular cases.
Gómez Plata, A. R. +2 more
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Reachability of fractional dynamical systems using ψ-Hilfer pseudo-fractional derivative [PDF]
Journal of Mathematical Physics, 2021 In this paper, we investigate the reachability of linear and non-linear systems in the sense of the ψ-Hilfer pseudo-fractional derivative in g-calculus by means of the Mittag–Leffler functions (one and two parameters). In this sense, two numerical examples are discussed in order to elucidate the investigated results.
J. Vanterler da C. Sousa +3 more
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$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 +2 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. +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 +2 more
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Space-time fractional reaction-diffusion equations associated with a generalized Riemann-Liouville fractional derivative [PDF]
, 2014 This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann-
Haubold, H. J. +2 more
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