Results 31 to 40 of about 485,864 (198)
Concept and application of interval-valued fractional conformable calculus
Alexandria Engineering Journal, 2022 This paper introduces a new concept of Caputo type interval-valued fractional conformable calculus. Based on this, some theorems and properties related to fractional conformable calculus are presented.
Lihong Zhang +3 more
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Journal of Function Spaces, 2021 A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson method, and ...
Lili Li, Mianfu She, Yuanling Niu
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Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
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Gronwall's Inequality in n Independent Variables [PDF]
Proceedings of the American Mathematical Society, 1973 The paper presents an extension of Gronwall's inequality to n independent variables. The inequality is established by solving a characteristic initial value problem by the Riemann method. Thus a Riemann function associated with a hyperbolic partial differential equation appears in the inequality.
openaire +1 more source
Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction
Abstract and Applied Analysis, 2013 This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive ...
Zheng Wu, Hao Huang, Lianglong Wang
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
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Journal of Taibah University for Science, 2019 In this note, we consider a nonlinear pantograph equation with Hilfer–Hadamard fractional derivative. We investigate the existence and continuous dependence results by using successive approximations and generalized Gronwall inequality.
D. Vivek, Kamal Shah, K. Kanagarajan
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Hyers-Ulam stability of a nonautonomous semilinear equation with fractional diffusion
Demonstratio Mathematica, 2020 In this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is
Villa-Morales José
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The present work is devoted to establishing existence results and examining the stability properties of solutions associated with a generalized Brusselator reaction–diffusion system in both the classical and fractional‐order settings. The corresponding ODE and PDE formulations are considered to establish the global existence of solutions in ...
Fadia Haouam +3 more
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On Volterra inequalities and their applications
International Journal of Mathematics and Mathematical Sciences, 2004 We present certain variants of two-dimensional and n-dimensional Volterra integral inequalities. In particular, generalizations of the Gronwall inequality are obtained.
Lechosław Hącia
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