Results 51 to 60 of about 695,650 (225)
Boundary value problems of fractional q-difference equations on the half-line
Boundary Value Problems, 2019 In this paper, we consider the boundary value problem of a class of nonlinear fractional q-difference equations involving the Riemann–Liouville fractional q-derivative on the half-line.
Kuikui Ma, Xinhui Li, Shurong Sun
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A nonlinear Liouville theorem for fractional equations in the Heisenberg group [PDF]
, 2015 We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant operators, which can be
E. Cinti, Jinggang Tan
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Gradient estimate and a Liouville theorem for a $p$-Laplacian evolution equation with a gradient nonlinearity [PDF]
Differential and Integral Equations, 2014 In this paper, we establish a local gradient estimate for a $p$-Lpalacian equation with a fast growing gradient nonlinearity. With this estimate, we can prove a parabolic Liouville theorem for ancient solutions satisfying some growth restriction near ...
Amal Attouchi
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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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A Lot of “Counterexamples” to Liouville's Theorem
Journal of Mathematical Analysis and Applications, 1996 We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any plane strip for every f ∈ M and for every derivation index j.
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A Liouville theorem for high order degenerate elliptic equations [PDF]
, 2014 In this paper, we apply the method of moving plane to the following high order degenerate elliptic equation, ( − A ) p u = u α in R + n + 1 , n ≥ 1 , where the operator A = y ∂ y 2 + a ∂ y + Δ x , a ≥ 1 .
Genggeng Huang, Congming Li
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Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
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Abstract and Applied Analysis, 2013 We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives.
Azizollah Babakhani +2 more
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Composition of Fractional Integral and Derivative Operators: Summarised in Tables
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption.
Arran Fernandez
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On Cauchy–Liouville-type theorems
Advances in Nonlinear Analysis, 2017 Abstract In this paper we explore Liouville-type theorems to solutions of PDEs involving the ϕ-Laplace operator in the setting of Orlicz–Sobolev spaces. Our results extend Liouville-type theorems that have been obtained recently.
Araya Ataklti, Mohammed Ahmed
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