Fractional Calculus and Applied Analysis
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Fractional differential inclusions in the Almgren sense
Fractional Calculus and Applied Analysis - Tập 18 Số 3 - Trang 673-686 - 2015
In this paper we study fractional differential inclusions in the sense of Almgren. We begin with a discussion of multiple-valued functions in the Almgren sense and include the basic results needed to make the paper selfcontained. Sufficient background on the fractional calculus is provided to make the material accessible also to the non-specialist readers. Our main result gives sufficient conditio......
Giải pháp Chu kỳ Tương đối cho Các Phương Trình Phát triển Phân số Kiểu Caputo Dịch bởi AI
Fractional Calculus and Applied Analysis - Tập 21 - Trang 1294-1312 - 2019
Trong bài báo này, chúng tôi chứng minh rằng các phương trình phát triển phân số tuyến tính kiểu Caputo không có nghiệm chu kỳ không hằng số. Sau đó, chúng tôi nghiên cứu các nghiệm chu kỳ tiệm cận của các phương trình phát triển phân số nửa tuyến tính và thiết lập các kết quả về sự tồn tại và duy nhất bằng cách sử dụng lý thuyết nhóm bán và các định lý điểm cố định. Cuối cùng, hai ví dụ được đưa ......
#phương trình phát triển phân số #nghiệm chu kỳ #lý thuyết nhóm bán #định lý điểm cố định #nghiệm tiệm cận
A non-local semilinear eigenvalue problem
Fractional Calculus and Applied Analysis - Tập 25 - Trang 2193-2221 - 2022
We prove that positive solutions of the fractional Lane–Emden equation with homogeneous Dirichlet boundary conditions satisfy pointwise estimates in terms of the best constant in Poincaré’s inequality on all open sets, and are isolated in
$$L^1$$
on smooth bounded ones, whence we deduce the isolat......
On the lifting property for the lipschitz spaces $$\varLambda _{\alpha }$$ with $$\alpha >0$$
Fractional Calculus and Applied Analysis - Tập 26 - Trang 351-369 - 2022
By combining suitable estimates for Bessel kernel and an interpolation argument, we give an alternative proof of the lifting property
$$\begin{aligned} (-\varDelta +1)^{-\alpha }: \varLambda _{\beta }\rightarrow \varLambda _{\beta +2\alpha } \quad \text{ is } \text{ an } \text{ isomorphism, } \end{aligned}$$
......
Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity
Fractional Calculus and Applied Analysis - - Trang 1-27 - 2024
In this paper, we consider the following problem
$$\begin{aligned} {\left\{ \begin{array}{ll} (-\varDelta )^{s} u=g(x) u^{2_{s}^{*}-1}+\lambda u^{-\gamma }, &{} \text { in } \varOmega , \\ u>0, \text { in } \varOmega , \quad u=0, &{} \text { on } \partial \varOmega , \end{array}\right. } \end{aligned}$$
where ......
Trace Inequalities for Fractional Integrals in Mixed Norm Grand Lebesgue Spaces
Fractional Calculus and Applied Analysis - Tập 23 - Trang 1452-1471 - 2020
D. Adams type trace inequalities for multiple fractional integral operators in grand Lebesgue spaces with mixed norms are established. Operators under consideration contain multiple fractional integrals defined on the product of quasi-metric measure spaces, and one-sided multiple potentials. In the case when we deal with operators defined on bounded sets, the established conditions are simultaneou......
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Fractional Calculus and Applied Analysis - Tập 15 - Trang 161-167 - 2012
Sum of series and new relations for Mittag-Leffler functions
Fractional Calculus and Applied Analysis - - 2024
An integral equation is constructed relating the three-parameter Mittag-Leffler function with a perturbed one, from which a new property is derived. The latter helps in finding new sums of series of Mittag-Leffler functions. Also, a bound is obtained for the Mittag-Leffler function, allowing to perform a sensitivity analysis, being vital in the solution of fractional differential equations. The bo......
Covariant fractional extension of the modified Laplace-operator used in 3D-shape recovery
Fractional Calculus and Applied Analysis - Tập 15 - Trang 332-343 - 2012
Extending the Liouville-Caputo definition of a fractional derivative to a nonlocal covariant generalization of arbitrary bound operators acting on multidimensional Riemannian spaces an appropriate approach for the 3D shape recovery of aperture afflicted 2D slide sequences is proposed. We demonstrate, that the step from a local to a nonlocal algorithm yields an order of magnitude in accuracy and by......
Infinitely many large solutions to a variable order nonlocal singular equation
Fractional Calculus and Applied Analysis - Tập 25 - Trang 822-839 - 2022
The paper establishes the existence of infinitely many large energy solutions for a nonlocal elliptic problem involving a variable exponent fractional
$$p(\cdot )$$
-Laplacian and a singularity, provided a positive parameter incorporated in the problem is sufficiently small. A variational method ca......
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