Results 11 to 20 of about 34,984 (270)
Implicit Fractional Differential Equations via the Liouville–Caputo Derivative [PDF]
Mathematics, 2015 We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.
Juan J. Nieto +2 more
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On stability for nonlinear implicit fractional differential equations
Le Matematiche, 2015 The purpose of this paper is to establish some types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of implicit fractional-order ...
Mouffak Benchohra, Jamal E. Lazreg
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Existence results for nonlinear implicit fractional differential equations [PDF]
Surveys in Mathematics and its Applications, 2014 In this paper, we establish the existence and uniqueness of solution for a class of initial value problem for implicit fractional differential equations with Caputo fractional derivative.
Mouffak Benchohra , Jamal Eddine Lazreg
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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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Nonlinear implicit differential equations of fractional order at resonance
Electronic Journal of Differential Equations, 2016 In this article, we obtain an existence result for periodic solutions to nonlinear implicit fractional differential equations with Caputo fractional derivatives. Our main tools is coincidence degree theory, which was first introduced by Mawhin.
Mouffak Benchohra +2 more
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Stability analysis for a class of implicit fractional differential equations involving Atangana-Baleanu fractional derivative. [PDF]
Adv Differ Equ, 2021 AbstractSome fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of ...
Asma, Shabbir S, Shah K, Abdeljawad T.
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On Implicit Time–Fractal–Fractional Differential Equation
Axioms, 2022 An implicit time–fractal–fractional differential equation involving the Atangana’s fractal–fractional derivative in the sense of Caputo with the Mittag–Leffler law type kernel is studied. Using the Banach fixed point theorem, the well-posedness of the solution is proved. We show that the solution exhibits an exponential growth bound, and, consequently,
McSylvester Ejighikeme Omaba +2 more
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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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On the impulsive implicit Ψ‐Hilfer fractional differential equations with delay [PDF]
Mathematical Methods in the Applied Sciences, 2019 In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam‐Hyers‐Mittag‐Leffler stability results for impulsive implicit Ψ‐Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam‐Hyers and generalized Ulam‐Hyers stability are the specific cases of Ulam‐Hyers‐Mittag‐Leffler stability ...
Jyoti P. Kharade, Kishor D. Kucche
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Some existence results on implicit fractional differential equations
Filomat, 2021 In this paper, we study the existence of a solution for the nonlinear implicit fractional differential equation of the type D?u(t) = f (t, u(t),D?u(t)), with Riemann-Liouville fractional derivative via the different boundary conditions u(0) = u(T), and the three point boundary conditions u(0) = ?1u(?) and u(T) = ?2u(?), where T > 0, t ...
V.V. Kharat +2 more
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