The Brezis–Nirenberg problem for fractional systems with Hardy potentials
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7856
Abstract: In this work, we study the existence of positive solutions to the following fractional elliptic systems with Hardy‐type singular potentials and coupled by critical homogeneous nonlinearities (−Δ)su−μ1u|x|2s=|u|2s∗−2u+ηα2s∗|u|α−2|v|βu+12Qu(u,v)inΩ,(−Δ)sv−μ2v|x|2s=|v|2s∗−2v+ηβ2s∗|u|α|v|β−2v+12Qv(u,v)inΩ,u,v>0inΩ,u=v=0inℝN\Ω, where (− Δ)s denotes the fractional Laplace operator, Ω⊂ℝN… read more here.
Keywords: brezis nirenberg; systems hardy; problem fractional; fractional systems ... See more keywords
Adaptive control for discontinuous variable-order fractional systems with disturbances
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DOI: 10.1007/s11071-021-06199-4
Abstract: This paper deals with the global asymptotic stabilization and finite-time stabilization issues for variable-order fractional systems with partial a priori bounded disturbances by designing an appropriate adaptive controller. Via the inductive method and Arzela-Ascoli theorem,… read more here.
Keywords: fractional systems; adaptive control; order fractional; variable order ... See more keywords
Cycles in asymptotically stable and chaotic fractional maps
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DOI: 10.1007/s11071-021-06379-2
Abstract: The presence of the power-law memory is a significant feature of many natural (biological, physical, etc.) and social systems. Continuous and discrete fractional calculus is the instrument to describe the behavior of systems with the… read more here.
Keywords: periodic points; stable chaotic; asymptotically periodic; asymptotically stable ... See more keywords
Numerical Solutions of Fractional Systems of Two-Point BVPs by Using the Iterative Reproducing Kernel Algorithm
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DOI: 10.1007/s11253-018-1526-8
Abstract: We propose an efficient computational method, namely, the iterative reproducing kernel method for the approximate solution of fractional-order systems of two-point time boundary-value problems in the Caputo sense. Two extended inner-product spaces are constructed in… read more here.
Keywords: reproducing kernel; fractional systems; solution; iterative reproducing ... See more keywords
The Exact Solutions of Fractional Differential Systems with n Sinusoidal Terms under Physical Conditions
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DOI: 10.3390/sym14122539
Abstract: This paper considers the classes of the first-order fractional differential systems containing a finite number n of sinusoidal terms. The fractional derivative employs the Riemann–Liouville fractional definition. As a method of solution, the Laplace transform… read more here.
Keywords: sinusoidal terms; fractional systems; differential systems; physical conditions ... See more keywords