Linear multistep methods for integrating reversible differential equations [PDF]
, 1999 This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem.
Kang F., N. Wyn Evans, Scott Tremaine
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Implicit Fractional Differential Equation Involving $\psi$–Caputo with Boundary Conditions [PDF]
Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES, 2021 This paper deals with the existence and uniqueness of solutions for boundary-value problems of the nonlinear \(\psi\)-Caputo fractional differential equations \[ \begin{aligned} ^CD^{\alpha, \psi}_{a^+}u(t) &= f(t, u(t),^CD^{\alpha, \psi}_{a^+}u(t)), \quad t\in [a, T],\\ u(T) &= \lambda u(\eta).
Abdellatif, Boutiara, Benbachir, Maamar
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Fourier spectral methods for fractional-in-space reaction-diffusion equations [PDF]
, 2012 Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity.
Bueno-Orovio, A., Burrage, K., Kay, D.
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On a nonlocal implicit problem under Atangana–Baleanu–Caputo fractional derivative
Boundary Value Problems, 2021 In this paper, we study a class of initial value problems for a nonlinear implicit fractional differential equation with nonlocal conditions involving the Atangana–Baleanu–Caputo fractional derivative.
Abeer S. Alnahdi +4 more
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Stability of Nonlinear Implicit Differential Equations with Caputo–Katugampola Fractional Derivative
Mathematics, 2023 The purpose of this paper is to study nonlinear implicit differential equations with the Caputo–Katugampola fractional derivative. By using Gronwall inequality and Banach fixed-point theorem, the existence of the solution of the implicit equation is ...
Qun Dai, Yunying Zhang
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Fractional Order Runge–Kutta Methods
Fractal and Fractional, 2023 This paper presents a new class of fractional order Runge–Kutta (FORK) methods for numerically approximating the solution of fractional differential equations (FDEs).
Farideh Ghoreishi +2 more
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Advances in Difference Equations, 2017 In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional ...
Akbar Zada, Sartaj Ali, Yongjin Li
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Implicit analytic solutions for a nonlinear fractional partial differential beam equation [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Konstantinos Liaskos +4 more
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Terminal Value Problem for Implicit Katugampola Fractional Differential Equations in b-Metric Spaces
Journal of Function Spaces, 2021 This manuscript deals with a class of Katugampola implicit fractional differential equations in b-metric spaces. The results are based on the α−φ-Geraghty type contraction and the fixed point theory. We express an illustrative example.
Salim Krim +3 more
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Qualitative Study on Solutions of Piecewise Nonlocal Implicit Fractional Differential Equations
Journal of Function Spaces, 2023 In this paper, we investigate new types of nonlocal implicit problems involving piecewise Caputo fractional operators. The existence and uniqueness results are proved by using some fixed point theorems. Furthermore, we present analogous results involving piecewise Caputo-Fabrizio and Atangana–Baleanu fractional operators.
Mohammed S. Abdo +5 more
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