Results 21 to 30 of about 1,341,149 (142)
, 2018 In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-boundary-value problem for linear and nonlinear time-fractional diffusion ...
Kirane, Mokhtar, Torebek, Berikbol T.
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Asian Journal of Control, Volume 28, Issue 1, Page 34-45, January 2026.Abstract We study a nonlinear ψ−$$ \psi - $$ Hilfer fractional‐order delay integro‐differential equation ( ψ−$$ \psi - $$ Hilfer FrODIDE) that incorporates N−$$ N- $$ multiple variable time delays. Utilizing the ψ−$$ \psi - $$ Hilfer fractional derivative ( ψ−$$ \psi - $$ Hilfer‐FrD), we investigate the Ulam–Hyers––Rassias (U–H–R), semi‐Ulam–Hyers ...
Cemil Tunç, Osman Tunç
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Studies on Fractional Differential Equations With Functional Boundary Condition by Inverse Operators
Mathematical Methods in the Applied Sciences, Volume 48, Issue 11, Page 11161-11170, 30 July 2025.ABSTRACT Fractional differential equations (FDEs) generalize classical integer‐order calculus to noninteger orders, enabling the modeling of complex phenomena that classical equations cannot fully capture. Their study has become essential across science, engineering, and mathematics due to their unique ability to describe systems with nonlocal ...
Chenkuan Li
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The Variable-Order Fractional Calculus of Variations
, 2018 This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the
Almeida, Ricardo +2 more
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Analytic Solution of a Class of Fractional Differential Equations [PDF]
, 2013 We consider the analytic solution of a class of fractional differential equations with variable coefficients by operatorial methods.
Yue Hu, Zuodong Yang
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Blowing‐Up Solution of a System of Fractional Differential Equations With Variable Order
Mathematical Methods in the Applied Sciences, Volume 48, Issue 9, Page 9726-9743, June 2025.ABSTRACT We investigated the necessary condition for blowing‐up solutions in finite time of the system u′(t)+(1)D0|tα(t)(u(t)−u0)=|v(t)|q,t>0,q>1,v′(t)+(1)D0|tβ(t)(v(t)−v0)=|u(t)|p,t>0,p>1$$ {u}^{\prime }(t)+{}_{(1)}{D}_{0\mid t}^{\alpha (t)}\left(u(t)-{u}_0\right)={\left|v(t)\right|}^q,\kern0.3em t>0,q>1,{v}^{\prime }(t)+{}_{(1)}{D}_{0\mid t}^{\beta ...
Muhammad Rizki Fadillah, Mokhtar Kirane
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Recovering discrete delayed fractional equations from trajectories
Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7630-7640, 15 May 2025.We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it has some delay effect or not and also to characterize the fractional component of the underlying generation model.
J. Alberto Conejero +2 more
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HMSFU: A hierarchical multi‐scale fusion unit for video prediction and beyond
IET Computer Vision, Volume 19, Issue 1, January/December 2025.A Hierarchical Multi‐Scale Fusion Unit (HMSFU) is proposed for video prediction. The HMSFU utilises a hierarchical multi‐scale architecture to capture rich contextual information, expand the receptive field of the entire network, and predict future possibilities at different granularity levels.
Hongchang Zhu, Faming Fang
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.The main objective of this research involves studying a new novel coupled pantograph system with fractional operators together with nonlocal antiperiodic integral boundary conditions. The system consists of nonlinear pantograph fractional equations which integrate with Caputo fractional operators and Hadamard integrals.
Gunaseelan Mani +4 more
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher‐order (q, τ)‐Bernoulli functions and polynomials. We build a robust basis for approximation in (q, τ)‐weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer‐type generating ...
Shaher Momani +2 more
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