Tiwari, Diksha; Mukhammadiev, Akbarali; Giordano, Paolo Hyper-power series and generalized real analytic functions. (English) Zbl 07802694 Monatsh. Math. 203, No. 2, 475-508 (2024). MSC: 46F30 26E30 PDFBibTeX XMLCite \textit{D. Tiwari} et al., Monatsh. Math. 203, No. 2, 475--508 (2024; Zbl 07802694) Full Text: DOI arXiv OA License
Khalili Golmankhaneh, Alireza; Welch, Kerri; Serpa, Cristina; Jørgensen, Palle E. T. Non-standard analysis for fractal calculus. (English) Zbl 07808296 J. Anal. 31, No. 3, 1895-1916 (2023). MSC: 28A80 34E18 26E35 PDFBibTeX XMLCite \textit{A. Khalili Golmankhaneh} et al., J. Anal. 31, No. 3, 1895--1916 (2023; Zbl 07808296) Full Text: DOI
Li, Min; Ming, Ju; Qin, Tingting; Zhou, Boya Convergence of an energy-preserving finite difference method for the nonlinear coupled space-fractional Klein-Gordon equations. (English) Zbl 07798645 Netw. Heterog. Media 18, No. 3, 957-981 (2023). MSC: 65M06 65N06 65M12 65M15 26A33 35R11 PDFBibTeX XMLCite \textit{M. Li} et al., Netw. Heterog. Media 18, No. 3, 957--981 (2023; Zbl 07798645) Full Text: DOI
Wang, Li; Tang, Liqin; Sun, Jijiang Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system. (English) Zbl 1511.35376 Fract. Calc. Appl. Anal. 26, No. 2, 672-693 (2023). MSC: 35R11 35Q61 47J30 26A33 PDFBibTeX XMLCite \textit{L. Wang} et al., Fract. Calc. Appl. Anal. 26, No. 2, 672--693 (2023; Zbl 1511.35376) Full Text: DOI
Cazacu, Cristian; Flynn, Joshua; Lam, Nguyen Caffarelli-Kohn-Nirenberg inequalities for curl-free vector fields and second order derivatives. (English) Zbl 1521.81120 Calc. Var. Partial Differ. Equ. 62, No. 4, Paper No. 118, 26 p. (2023). MSC: 81S07 26D10 46E35 26D15 58A10 17B10 PDFBibTeX XMLCite \textit{C. Cazacu} et al., Calc. Var. Partial Differ. Equ. 62, No. 4, Paper No. 118, 26 p. (2023; Zbl 1521.81120) Full Text: DOI arXiv
Stegliński, Robert On local and nonlocal discrete \(p\)-Laplacian equations via Clark’s theorem. (English) Zbl 1525.39005 Qual. Theory Dyn. Syst. 22, No. 2, Paper No. 73, 16 p. (2023). MSC: 39A12 39A13 39A14 35J92 35R11 26A33 PDFBibTeX XMLCite \textit{R. Stegliński}, Qual. Theory Dyn. Syst. 22, No. 2, Paper No. 73, 16 p. (2023; Zbl 1525.39005) Full Text: DOI
Costa, Augusto C. R.; Maia, Bráulio B. V.; Miyagaki, Olímpio H. On existence and concentration of solutions for Hamiltonian systems involving fractional operator with critical exponential growth. (English) Zbl 1528.37061 Math. Nachr. 295, No. 8, 1480-1512 (2022). MSC: 37K58 37K55 35R11 35Q55 26A33 PDFBibTeX XMLCite \textit{A. C. R. Costa} et al., Math. Nachr. 295, No. 8, 1480--1512 (2022; Zbl 1528.37061) Full Text: DOI
Guo, Zhao Solving 3D fractional Schrödinger systems on the basis of Phragmén-Lindelöf methods. (English) Zbl 1503.35261 Fract. Calc. Appl. Anal. 25, No. 5, 1925-1953 (2022). MSC: 35R11 35Q55 26A33 PDFBibTeX XMLCite \textit{Z. Guo}, Fract. Calc. Appl. Anal. 25, No. 5, 1925--1953 (2022; Zbl 1503.35261) Full Text: DOI
Benci, Vieri An improved setting for generalized functions: fine ultrafunctions. (English) Zbl 1503.35063 Milan J. Math. 90, No. 2, 575-646 (2022). MSC: 35D30 03H05 26E30 46T30 PDFBibTeX XMLCite \textit{V. Benci}, Milan J. Math. 90, No. 2, 575--646 (2022; Zbl 1503.35063) Full Text: DOI arXiv
Alam, Irfan Limiting spherical integrals of bounded continuous functions. (English) Zbl 1525.28010 J. Theor. Probab. 35, No. 4, 2304-2342 (2022). MSC: 28E05 03H05 26E35 28C20 46S20 PDFBibTeX XMLCite \textit{I. Alam}, J. Theor. Probab. 35, No. 4, 2304--2342 (2022; Zbl 1525.28010) Full Text: DOI arXiv
Nguyen Minh Dien; Tran Quoc Viet On mild solutions of the p-Laplacian fractional Langevin equations with anti-periodic type boundary conditions. (English) Zbl 1524.34143 Int. J. Comput. Math. 99, No. 9, 1823-1848 (2022). MSC: 34G20 34A08 26A33 34B15 47N20 34B08 PDFBibTeX XMLCite \textit{Nguyen Minh Dien} and \textit{Tran Quoc Viet}, Int. J. Comput. Math. 99, No. 9, 1823--1848 (2022; Zbl 1524.34143) Full Text: DOI
Benci, Vieri; Cococcioni, Marco; Fiaschi, Lorenzo Non-standard analysis revisited: an easy axiomatic presentation oriented towards numerical applications. (English) Zbl 1515.03232 Int. J. Appl. Math. Comput. Sci. 32, No. 1, 65-80 (2022). MSC: 03H05 26E35 PDFBibTeX XMLCite \textit{V. Benci} et al., Int. J. Appl. Math. Comput. Sci. 32, No. 1, 65--80 (2022; Zbl 1515.03232) Full Text: DOI
Bottazzi, Emanuele A real-valued measure on non-Archimedean field extensions of \(\mathbb{R}\). (English) Zbl 1494.26063 \(p\)-Adic Numbers Ultrametric Anal. Appl. 14, No. 1, 14-43 (2022). MSC: 26E30 12J25 28E05 PDFBibTeX XMLCite \textit{E. Bottazzi}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 14, No. 1, 14--43 (2022; Zbl 1494.26063) Full Text: DOI arXiv
Tiwari, Diksha; Giordano, Paolo Hyperseries in the non-Archimedean ring of Colombeau generalized numbers. (English) Zbl 1508.46032 Monatsh. Math. 197, No. 1, 193-223 (2022). MSC: 46F30 26E30 PDFBibTeX XMLCite \textit{D. Tiwari} and \textit{P. Giordano}, Monatsh. Math. 197, No. 1, 193--223 (2022; Zbl 1508.46032) Full Text: DOI arXiv
Scandone, Raffaele; Luperi Baglini, Lorenzo; Simonov, Kyrylo A characterization of singular Schrödinger operators on the half-line. (English) Zbl 1485.34207 Can. Math. Bull. 64, No. 4, 923-941 (2021). MSC: 34L40 34E15 26E35 47S20 PDFBibTeX XMLCite \textit{R. Scandone} et al., Can. Math. Bull. 64, No. 4, 923--941 (2021; Zbl 1485.34207) Full Text: DOI arXiv
Benci, Vieri; Cococcioni, Marco The algorithmic numbers in non-Archimedean numerical computing environments. (English) Zbl 07439617 Discrete Contin. Dyn. Syst., Ser. S 14, No. 5, 1673-1692 (2021). MSC: 65Y04 26E30 26E35 PDFBibTeX XMLCite \textit{V. Benci} and \textit{M. Cococcioni}, Discrete Contin. Dyn. Syst., Ser. S 14, No. 5, 1673--1692 (2021; Zbl 07439617) Full Text: DOI
Bottazzi, Emanuele; Katz, Mikhail G. Infinitesimals via Cauchy sequences: refining the classical equivalence. (English) Zbl 1484.26111 Open Math. 19, 477-482 (2021). MSC: 26E35 PDFBibTeX XMLCite \textit{E. Bottazzi} and \textit{M. G. Katz}, Open Math. 19, 477--482 (2021; Zbl 1484.26111) Full Text: DOI arXiv
Mukhammadiev, A.; Tiwari, D.; Apaaboah, G.; Giordano, P. Supremum, infimum and hyperlimits in the non-Archimedean ring of Colombeau generalized numbers. (English) Zbl 1483.46042 Monatsh. Math. 196, No. 1, 163-190 (2021). Reviewer: Michael Kunzinger (Wien) MSC: 46F30 26E30 PDFBibTeX XMLCite \textit{A. Mukhammadiev} et al., Monatsh. Math. 196, No. 1, 163--190 (2021; Zbl 1483.46042) Full Text: DOI arXiv
Mederski, Jarosław; Szulkin, Andrzej A Sobolev-type inequality for the curl operator and ground states for the curl-curl equation with critical Sobolev exponent. (English) Zbl 1475.35332 Arch. Ration. Mech. Anal. 241, No. 3, 1815-1842 (2021). MSC: 35Q61 35Q30 35Q55 78A25 35J20 35B33 26D10 PDFBibTeX XMLCite \textit{J. Mederski} and \textit{A. Szulkin}, Arch. Ration. Mech. Anal. 241, No. 3, 1815--1842 (2021; Zbl 1475.35332) Full Text: DOI arXiv
Khater, Mostafa M. A.; Baleanu, Dumitru On abundant new solutions of two fractional complex models. (English) Zbl 1482.35252 Adv. Difference Equ. 2020, Paper No. 268, 14 p. (2020). MSC: 35R11 35Q53 26A33 35C08 76U65 PDFBibTeX XMLCite \textit{M. M. A. Khater} and \textit{D. Baleanu}, Adv. Difference Equ. 2020, Paper No. 268, 14 p. (2020; Zbl 1482.35252) Full Text: DOI
Yu, Yuanyang; Zhao, Fukun; Zhao, Leiga Positive and sign-changing least energy solutions for a fractional Schrödinger-Poisson system with critical exponent. (English) Zbl 1448.35425 Appl. Anal. 99, No. 13, 2229-2257 (2020). MSC: 35Q40 35J50 58E05 81Q05 35B33 35B10 35R11 26A33 PDFBibTeX XMLCite \textit{Y. Yu} et al., Appl. Anal. 99, No. 13, 2229--2257 (2020; Zbl 1448.35425) Full Text: DOI
Bottazzi, Emanuele Spaces of measurable functions on the Levi-Civita field. (English) Zbl 1454.26045 Indag. Math., New Ser. 31, No. 4, 650-694 (2020). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 26E30 46S10 PDFBibTeX XMLCite \textit{E. Bottazzi}, Indag. Math., New Ser. 31, No. 4, 650--694 (2020; Zbl 1454.26045) Full Text: DOI arXiv
Jin, Tiankun; Yang, Zhipeng The fractional Schrödinger-Poisson systems with infinitely many solutions. (English) Zbl 1437.35597 J. Korean Math. Soc. 57, No. 2, 489-506 (2020). MSC: 35Q40 35J50 58E05 26A33 35R11 PDFBibTeX XMLCite \textit{T. Jin} and \textit{Z. Yang}, J. Korean Math. Soc. 57, No. 2, 489--506 (2020; Zbl 1437.35597) Full Text: DOI
Benci, Vieri; Luperi Baglini, Lorenzo; Squassina, Marco Generalized solutions of variational problems and applications. (English) Zbl 1414.26051 Adv. Nonlinear Anal. 9, 124-147 (2020). MSC: 26E35 28E05 46S20 PDFBibTeX XMLCite \textit{V. Benci} et al., Adv. Nonlinear Anal. 9, 124--147 (2020; Zbl 1414.26051) Full Text: DOI arXiv
Ozturk, Okkes; Yilmazer, Resat Solutions of the radial Schrödinger equation in hypergeometric and discrete fractional forms. (English) Zbl 1487.39005 Commun. Fac. Sci. Univ. Ank., Sér. A1, Math. Stat. 68, No. 1, 833-839 (2019). MSC: 39A12 26A33 35J10 47B39 PDFBibTeX XMLCite \textit{O. Ozturk} and \textit{R. Yilmazer}, Commun. Fac. Sci. Univ. Ank., Sér. A1, Math. Stat. 68, No. 1, 833--839 (2019; Zbl 1487.39005) Full Text: DOI
Bottazzi, Emanuele Grid functions of nonstandard analysis in the theory of distributions and in partial differential equations. (English) Zbl 1423.46056 Adv. Math. 345, 429-482 (2019); corrigendum ibid. 427, Article ID 109133, 2 p. (2023). Reviewer: Eduard Nigsch (Wien) MSC: 46F30 46S20 26E35 03H05 PDFBibTeX XMLCite \textit{E. Bottazzi}, Adv. Math. 345, 429--482 (2019; Zbl 1423.46056) Full Text: DOI arXiv
Abdeljalil, Saghe A new approach to nonstandard analysis. (English) Zbl 1412.26065 Sahand Commun. Math. Anal. 12, No. 1, 195-254 (2018). MSC: 26E35 03H05 PDFBibTeX XMLCite \textit{S. Abdeljalil}, Sahand Commun. Math. Anal. 12, No. 1, 195--254 (2018; Zbl 1412.26065) Full Text: DOI
Dawson, C. Bryan A new extension of the Riemann integral. (English) Zbl 1392.26039 Am. Math. Mon. 125, No. 2, 130-140 (2018). MSC: 26E35 26A42 PDFBibTeX XMLCite \textit{C. B. Dawson}, Am. Math. Mon. 125, No. 2, 130--140 (2018; Zbl 1392.26039) Full Text: DOI
Benci, Vieri; Baglini, Lorenzo Luperi A topological approach to non-Archimedean mathematics. (English) Zbl 1351.26046 Gazzola, Filippo (ed.) et al., Geometric properties for parabolic and elliptic PDE’s. Contributions of the 4th Italian-Japanese workshop, GPPEPDEs, Palinuro, Italy, May 25–29, 2015. Cham: Springer (ISBN 978-3-319-41536-9/hbk; 978-3-319-41538-3/ebook). Springer Proceedings in Mathematics & Statistics 176, 17-40 (2016). MSC: 26E30 26E35 54A20 PDFBibTeX XMLCite \textit{V. Benci} and \textit{L. L. Baglini}, Springer Proc. Math. Stat. 176, 17--40 (2016; Zbl 1351.26046) Full Text: DOI arXiv
Chen, Jing; Tang, Xian Hua Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation. (English) Zbl 1374.35420 Appl. Math., Praha 60, No. 6, 703-724 (2015). MSC: 35R11 26A33 35G60 PDFBibTeX XMLCite \textit{J. Chen} and \textit{X. H. Tang}, Appl. Math., Praha 60, No. 6, 703--724 (2015; Zbl 1374.35420) Full Text: DOI Link
Benci, Vieri; Luperi Baglini, Lorenzo Generalized functions beyond distributions. (English) Zbl 1331.26051 Arab. J. Math. 4, No. 4, 231-253 (2015). MSC: 26E30 26E35 46F30 PDFBibTeX XMLCite \textit{V. Benci} and \textit{L. Luperi Baglini}, Arab. J. Math. 4, No. 4, 231--253 (2015; Zbl 1331.26051) Full Text: DOI arXiv
Weiss, Ittay Survey article: The real numbers – a survey of constructions. (English) Zbl 1386.26002 Rocky Mt. J. Math. 45, No. 3, 737-762 (2015). MSC: 26A03 11A63 00A05 PDFBibTeX XMLCite \textit{I. Weiss}, Rocky Mt. J. Math. 45, No. 3, 737--762 (2015; Zbl 1386.26002) Full Text: DOI arXiv Euclid
Benci, Vieri; Nisoli, Isaia Towards a Morse theory on Banach spaces via ultrafunctions. (English) Zbl 1317.58015 Arab J. Math. Sci. 21, No. 2, 144-158 (2015). MSC: 58E05 26E30 26E35 35D99 35A15 PDFBibTeX XMLCite \textit{V. Benci} and \textit{I. Nisoli}, Arab J. Math. Sci. 21, No. 2, 144--158 (2015; Zbl 1317.58015) Full Text: DOI arXiv
Benci, Vieri; Luperi Baglini, Lorenzo A non-Archimedean algebra and the Schwartz impossibility theorem. (English) Zbl 1321.46045 Monatsh. Math. 176, No. 4, 503-520 (2015). Reviewer: Deshna Loonker (Jodhpur) MSC: 46F30 26E30 26E35 13N99 PDFBibTeX XMLCite \textit{V. Benci} and \textit{L. Luperi Baglini}, Monatsh. Math. 176, No. 4, 503--520 (2015; Zbl 1321.46045) Full Text: DOI arXiv
Benci, Vieri; Bottazzi, Emanuele; Di Nasso, Mauro Some applications of numerosities in measure theory. (English) Zbl 1309.26028 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 26, No. 1, 37-47 (2015). MSC: 26E30 28E15 26E35 60A05 PDFBibTeX XMLCite \textit{V. Benci} et al., Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 26, No. 1, 37--47 (2015; Zbl 1309.26028) Full Text: DOI arXiv
Benci, Vieri; Bottazzi, Emanuele; Di Nasso, Mauro Elementary numerosity and measures. (English) Zbl 1300.26018 J. Log. Anal. 6, Paper No. 3, 14 p. (2014). MSC: 26E30 28E15 26E35 60A05 PDFBibTeX XMLCite \textit{V. Benci} et al., J. Log. Anal. 6, Paper No. 3, 14 p. (2014; Zbl 1300.26018) Full Text: DOI arXiv
Benci, Vieri; Baglini, Lorenzo Luperi Ultrafunctions and applications. (English) Zbl 1290.26038 Discrete Contin. Dyn. Syst., Ser. S 7, No. 4, 593-616 (2014). MSC: 26E30 26E35 46F30 PDFBibTeX XMLCite \textit{V. Benci} and \textit{L. L. Baglini}, Discrete Contin. Dyn. Syst., Ser. S 7, No. 4, 593--616 (2014; Zbl 1290.26038) Full Text: DOI arXiv
Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics. (English) Zbl 1392.03012 Found. Sci. 18, No. 2, 259-296 (2013). MSC: 03A05 00A30 03H05 26E35 PDFBibTeX XMLCite \textit{V. Kanovei} et al., Found. Sci. 18, No. 2, 259--296 (2013; Zbl 1392.03012) Full Text: DOI arXiv
Błaszczyk, Piotr; Katz, Mikhail G.; Sherry, David Ten misconceptions from the history of analysis and their debunking. (English) Zbl 1291.01018 Found. Sci. 18, No. 1, 43-74 (2013). Reviewer: Thomas Sonar (Braunschweig) MSC: 01A55 26-03 PDFBibTeX XMLCite \textit{P. Błaszczyk} et al., Found. Sci. 18, No. 1, 43--74 (2013; Zbl 1291.01018) Full Text: DOI arXiv
Benci, Vieri Ultrafunctions and generalized solutions. (English) Zbl 1273.26035 Adv. Nonlinear Stud. 13, No. 2, 461-486 (2013). MSC: 26E30 26E35 35D99 81Q99 PDFBibTeX XMLCite \textit{V. Benci}, Adv. Nonlinear Stud. 13, No. 2, 461--486 (2013; Zbl 1273.26035) Full Text: DOI arXiv
Forti, Marco A simple algebraic characterization of nonstandard extensions. (English) Zbl 1288.03050 Proc. Am. Math. Soc. 140, No. 8, 2903-2912 (2012). Reviewer: Isaac Goldbring (Chicago) MSC: 03H05 03C07 03C20 26E35 PDFBibTeX XMLCite \textit{M. Forti}, Proc. Am. Math. Soc. 140, No. 8, 2903--2912 (2012; Zbl 1288.03050) Full Text: DOI arXiv
Dasgupta, Abhijit A set of axioms for nonstandard extensions. (English) Zbl 1235.26019 Math. Log. Q. 57, No. 5, 485-493 (2011). Reviewer: Isaac Goldbring (Los Angeles) MSC: 26E35 03H05 03C20 PDFBibTeX XMLCite \textit{A. Dasgupta}, Math. Log. Q. 57, No. 5, 485--493 (2011; Zbl 1235.26019) Full Text: DOI
Giordano, Paolo Fermat-Reyes method in the ring of Fermat reals. (English) Zbl 1238.03052 Adv. Math. 228, No. 2, 862-893 (2011). Reviewer: Isaac Goldbring (Los Angeles) MSC: 03H05 26E35 PDFBibTeX XMLCite \textit{P. Giordano}, Adv. Math. 228, No. 2, 862--893 (2011; Zbl 1238.03052) Full Text: DOI
Giordano, P. Infinitesimals without logic. (English) Zbl 1264.26035 Russ. J. Math. Phys. 17, No. 2, 159-191 (2010). Reviewer: Isaac Goldbring (Chicago) MSC: 26E35 03H05 PDFBibTeX XMLCite \textit{P. Giordano}, Russ. J. Math. Phys. 17, No. 2, 159--191 (2010; Zbl 1264.26035) Full Text: DOI arXiv
Giordano, Paolo The ring of Fermat reals. (English) Zbl 1205.26051 Adv. Math. 225, No. 4, 2050-2075 (2010). Reviewer: Stefan G. Samko (Faro) MSC: 26E99 03H05 26E35 PDFBibTeX XMLCite \textit{P. Giordano}, Adv. Math. 225, No. 4, 2050--2075 (2010; Zbl 1205.26051) Full Text: DOI
Sergeyev, Yaroslav D. Numerical point of view on calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains. (English) Zbl 1238.28013 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e1688-e1707 (2009). MSC: 28E99 00A30 26A03 03E10 PDFBibTeX XMLCite \textit{Y. D. Sergeyev}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e1688--e1707 (2009; Zbl 1238.28013) Full Text: DOI arXiv
Benci, Vieri; Di Nasso, Mauro A purely algebraic characterization of the hyperreal numbers. (English) Zbl 1113.26028 Proc. Am. Math. Soc. 133, No. 9, 2501-2505 (2005). MSC: 26E35 16S60 54C40 PDFBibTeX XMLCite \textit{V. Benci} and \textit{M. Di Nasso}, Proc. Am. Math. Soc. 133, No. 9, 2501--2505 (2005; Zbl 1113.26028) Full Text: DOI
Benci, Vieri; Di Nasso, Mauro Alpha-theory: An elementary axiomatics for nonstandard analysis. (English) Zbl 1038.26019 Expo. Math. 21, No. 4, 355-386 (2003). Reviewer: W. A. J. Luxemburg (Pasadena) MSC: 26E35 03H05 PDFBibTeX XMLCite \textit{V. Benci} and \textit{M. Di Nasso}, Expo. Math. 21, No. 4, 355--386 (2003; Zbl 1038.26019) Full Text: DOI
Chang, Kung-Ching Variational methods for non-differentiable functionals and their applications to partial differential equations. (English) Zbl 0487.49027 J. Math. Anal. Appl. 80, 102-129 (1981). MSC: 49Q20 58E05 28A15 26B35 35J60 35R05 PDFBibTeX XMLCite \textit{K.-C. Chang}, J. Math. Anal. Appl. 80, 102--129 (1981; Zbl 0487.49027) Full Text: DOI