Caputo generalized psi-fractional integral inequalities

• Autorzy: Anastassiou George A.

Identyfikatory

DOI

10.1515/jaa-2020-2037

• Języki publikacji: EN

Abstrakty

EN

Very general univariate and multivariate Caputo ψ-fractional integral inequalities of Poincaré, Sobolev and Hilbert-Pachpatte types are presented. Estimates are with respect to ‖ ⋅ ‖p, 1 ≤ p < ∞. Applications are given.

Słowa kluczowe

EN

Poincare inequalities; Sobolev inequalities; Hilbert-Pachpatte inequalities; right Caputo psi-fractional derivatives; left Caputo psi-fractional derivatives; polar coordinates method

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2021
• Tom: Vol. 27, nr 1
• Strony: 107--120
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Anastassiou George A.

• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

Bibliografia

• [1] G. Acosta and R. G. Durán, An optimal Poincaré inequality in L󸀠 for convex domains, Proc. Amer. Math. Soc. 132 (2003), no. 1, 195-202.
• [2] R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simul. 44 (2017), 460-481.
• [3] G. A. Anastassiou, Fractional Differentiation Inequalities, Springer, New York, 2009.
• [4] G. A. Anastassiou, Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations, Springer, Heidelberg, 2018.
• [5] L. C. Evans, Partial Differential Equations, Grad. Stud. Math. 19, American Mathematical Society, Providence, 1998.
• [6] B. G. Pachpatte, Inequalities similar to the integral analogue of Hilbert’s inequalities, Tamkang J. Math. 30 (1999), no. 1, 139-146.
• [7] W. Rudin, Real and Complex Analysis, Mc Graw Hill, London, 1970.
• [8] D. Stroock, A Concise Introduction to the Theory of Integration, 3rd ed., Birkäuser, Boston, 1999.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)