Results 11 to 20 of about 10,319 (253)
Local integration by parts and Pohozaev identities for higher order fractional Laplacians
Discrete and Continuous Dynamical Systems, 2015 The sign of the boundary term in Theorem 1.5 has been ...
Xavier Ros-Oton, Joaquim Serra
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Journal of Functional Analysis, 2016 We consider the fractional Laplacian operator $(-Δ)^s$ (let $ s \in (0,1) $) on Euclidean space and investigate the validity of the classical integration-by-parts formula that connects the $ L^2(\mathbb{R}^d) $ scalar product between a function and its fractional Laplacian to the nonlocal norm of the fractional Sobolev space $ \dot{H}^s(\mathbb{R}^d) $.
Matteo Muratori
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On Certain Integrals Related to Saran’s Hypergeometric Function FK
Fractal and Fractional, 2022 In the present paper, we establish two Erdélyi-type integrals for Saran’s hypergeometric function FK, which has applications in specific branches of applied physics and statistics (see below).
Minjie Luo +2 more
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Nonexistence of global solutions for a Hilfer–Katugampola fractional differential problem
Partial Differential Equations in Applied Mathematics, 2023 The aim of this paper is to investigate the absence of global solutions for a fractional differential problem involving a generalized Katugampola derivative.
Sandeep P. Bhairat, Mohammad E. Samei
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Hardy-Leindler-Type Inequalities via Conformable Delta Fractional Calculus
Journal of Function Spaces, 2022 In this article, some fractional Hardy-Leindler-type inequalities will be illustrated by utilizing the chain law, Hölder’s inequality, and integration by parts on fractional time scales.
H. M. Rezk +6 more
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The General Fractional Integrals and Derivatives on a Finite Interval
Mathematics, 2023 The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis.
Mohammed Al-Refai, Yuri Luchko
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On the sub–diffusion fractional initial value problem with time variable order
Advances in Nonlinear Analysis, 2021 We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a ...
Cuesta Eduardo +3 more
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On the Basic Theory of Some Generalized and Fractional Derivatives
Fractal and Fractional, 2022 We continue the development of the basic theory of generalized derivatives as introduced and give some of their applications. In particular, we formulate necessary conditions for extrema, Rolle’s theorem, the mean value theorem, the fundamental theorem ...
Leila Gholizadeh Zivlaei +1 more
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A Variety of Nabla Hardy’s Type Inequality on Time Scales
Mathematics, 2022 The primary goal of this research is to prove some new Hardy-type ∇-conformable dynamic inequalities by employing product rule, integration by parts, chain rule and (γ,a)-nabla Hölder inequality on time scales.
Ahmed A. El-Deeb +3 more
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Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel [PDF]
, 2016 In this manuscript we define the right fractional derivative and its corresponding right fractional integral for the recently introduced nonlocal fractional derivative with Mittag-Leffler kernel.
T. Abdeljawad, D. Baleanu
semanticscholar +1 more source