Valarmathi, R.; Gowrisankar, A. Variable order fractional calculus on \(\alpha\)-fractal functions. (English) Zbl 07822484 J. Anal. 31, No. 4, 2799-2815 (2023). MSC: 28A80 26A33 41A05 PDFBibTeX XMLCite \textit{R. Valarmathi} and \textit{A. Gowrisankar}, J. Anal. 31, No. 4, 2799--2815 (2023; Zbl 07822484) Full Text: DOI
Li, Jing; Qi, Jiangang Continuous dependence of eigenvalues on potential functions for nonlocal Sturm-Liouville equations. (English) Zbl 07783877 Math. Methods Appl. Sci. 46, No. 9, 10617-10623 (2023). MSC: 34B09 PDFBibTeX XMLCite \textit{J. Li} and \textit{J. Qi}, Math. Methods Appl. Sci. 46, No. 9, 10617--10623 (2023; Zbl 07783877) Full Text: DOI
Han, Zhaolong; Tian, Xiaochuan Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications. (English) Zbl 07778941 Math. Models Methods Appl. Sci. 33, No. 12, 2507-2556 (2023). MSC: 47B92 46E35 PDFBibTeX XMLCite \textit{Z. Han} and \textit{X. Tian}, Math. Models Methods Appl. Sci. 33, No. 12, 2507--2556 (2023; Zbl 07778941) Full Text: DOI arXiv
Valarmathi, R.; Gowrisankar, A. On the variable order fractional calculus of fractal interpolation functions. (English) Zbl 1522.26008 Fract. Calc. Appl. Anal. 26, No. 3, 1273-1293 (2023). MSC: 26A33 41A05 PDFBibTeX XMLCite \textit{R. Valarmathi} and \textit{A. Gowrisankar}, Fract. Calc. Appl. Anal. 26, No. 3, 1273--1293 (2023; Zbl 1522.26008) Full Text: DOI
Chandra, Subhash; Abbas, Syed; Liang, Yongshun On the box dimension of Weyl-Marchaud fractional derivative and linearity effect. (English) Zbl 07726800 Fractals 31, No. 5, Article ID 2350058, 8 p. (2023). MSC: 26A33 28A78 PDFBibTeX XMLCite \textit{S. Chandra} et al., Fractals 31, No. 5, Article ID 2350058, 8 p. (2023; Zbl 07726800) Full Text: DOI
Priyanka, T. M. C.; Gowrisankar, A. Construction of new affine and non-affine fractal interpolation functions through the Weyl-Marchaud derivative. (English) Zbl 07726784 Fractals 31, No. 5, Article ID 2350041, 15 p. (2023). MSC: 28A80 26A33 41A05 PDFBibTeX XMLCite \textit{T. M. C. Priyanka} and \textit{A. Gowrisankar}, Fractals 31, No. 5, Article ID 2350041, 15 p. (2023; Zbl 07726784) Full Text: DOI
Li, Kun Yuan; Yao, Kui; Zhang, Kai On the fractional derivative of a type of self-affine curves. (English) Zbl 07726782 Fractals 31, No. 5, Article ID 2350039, 7 p. (2023). MSC: 26A33 28A80 28A78 PDFBibTeX XMLCite \textit{K. Y. Li} et al., Fractals 31, No. 5, Article ID 2350039, 7 p. (2023; Zbl 07726782) Full Text: DOI
Priyanka, T. M. C.; Agathiyan, A.; Gowrisankar, A. Weyl-Marchaud fractional derivative of a vector valued fractal interpolation function with function contractivity factors. (English) Zbl 1524.28018 J. Anal. 31, No. 1, 657-689 (2023). MSC: 28A80 26A33 41A05 PDFBibTeX XMLCite \textit{T. M. C. Priyanka} et al., J. Anal. 31, No. 1, 657--689 (2023; Zbl 1524.28018) Full Text: DOI
Xu, Xiaoyan; Yu, Xianye The fractional smoothness of integral functionals driven by Brownian motion. (English) Zbl 1499.60173 Stat. Probab. Lett. 193, Article ID 109717, 11 p. (2023). MSC: 60H07 60G15 60J55 PDFBibTeX XMLCite \textit{X. Xu} and \textit{X. Yu}, Stat. Probab. Lett. 193, Article ID 109717, 11 p. (2023; Zbl 1499.60173) Full Text: DOI
Yao, Kui; Chen, Haotian; Peng, W. L.; Wang, Zekun; Yao, Jia; Wu, Yipeng A new method on box dimension of Weyl-Marchaud fractional derivative of Weierstrass function. (English) Zbl 1496.26007 Chaos Solitons Fractals 142, Article ID 110317, 6 p. (2021). MSC: 26A33 26A27 28A80 PDFBibTeX XMLCite \textit{K. Yao} et al., Chaos Solitons Fractals 142, Article ID 110317, 6 p. (2021; Zbl 1496.26007) Full Text: DOI
Priyanka, T. M. C.; Gowrisankar, A. Analysis on Weyl-Marchaud fractional derivative for types of fractal interpolation function with fractal dimension. (English) Zbl 1511.28007 Fractals 29, No. 7, Article ID 2150215, 24 p. (2021). MSC: 28A80 26A33 41A05 PDFBibTeX XMLCite \textit{T. M. C. Priyanka} and \textit{A. Gowrisankar}, Fractals 29, No. 7, Article ID 2150215, 24 p. (2021; Zbl 1511.28007) Full Text: DOI
Chandra, Subhash; Abbas, Syed Analysis of mixed Weyl-Marchaud fractional derivative and box dimensions. (English) Zbl 1491.28003 Fractals 29, No. 6, Article ID 2150145, 13 p. (2021). MSC: 28A78 26A33 PDFBibTeX XMLCite \textit{S. Chandra} and \textit{S. Abbas}, Fractals 29, No. 6, Article ID 2150145, 13 p. (2021; Zbl 1491.28003) Full Text: DOI
Ferrari, Fausto Some extension results for nonlocal operators and applications. (English) Zbl 1472.35432 Beghin, Luisa (ed.) et al., Nonlocal and fractional operators. Selected papers based on the presentations at the international workshop, Rome, Italy, April 12–13, 2019. Cham: Springer. SEMA SIMAI Springer Ser. 26, 155-187 (2021). MSC: 35R11 26A33 PDFBibTeX XMLCite \textit{F. Ferrari}, SEMA SIMAI Springer Ser. 26, 155--187 (2021; Zbl 1472.35432) Full Text: DOI
Yakhshiboev, Makhmadiyor U. \(\Psi\)-Marchaud-Hadamard-type fractional derivative and the inversion of \(\Psi\)-Hadamard-type fractional integrals. (English) Zbl 1488.26030 Uzb. Math. J. 2020, No. 3, 141-162 (2020). MSC: 26A33 46E30 PDFBibTeX XMLCite \textit{M. U. Yakhshiboev}, Uzb. Math. J. 2020, No. 3, 141--162 (2020; Zbl 1488.26030)
Stefański, Tomasz P.; Gulgowski, Jacek Signal propagation in electromagnetic media described by fractional-order models. (English) Zbl 1451.78013 Commun. Nonlinear Sci. Numer. Simul. 82, Article ID 105029, 16 p. (2020). MSC: 78A25 78A40 35R11 26A33 78M99 65T50 PDFBibTeX XMLCite \textit{T. P. Stefański} and \textit{J. Gulgowski}, Commun. Nonlinear Sci. Numer. Simul. 82, Article ID 105029, 16 p. (2020; Zbl 1451.78013) Full Text: DOI
Stinga, Pablo Raúl; Vaughan, Mary One-sided fractional derivatives, fractional Laplacians, and weighted Sobolev spaces. (English) Zbl 1436.26007 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 193, Article ID 111505, 29 p. (2020). MSC: 26A33 26A24 35R11 42B25 46E35 PDFBibTeX XMLCite \textit{P. R. Stinga} and \textit{M. Vaughan}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 193, Article ID 111505, 29 p. (2020; Zbl 1436.26007) Full Text: DOI arXiv
Yakhshiboev, Makhmadiyor U. A Chen-type modification of ball fractional integro-differentiation. (English) Zbl 1488.26028 Uzb. Math. J. 2019, No. 2, 135-153 (2019). MSC: 26A33 PDFBibTeX XMLCite \textit{M. U. Yakhshiboev}, Uzb. Math. J. 2019, No. 2, 135--153 (2019; Zbl 1488.26028) Full Text: DOI
Liang, Y. S.; Liu, N. Fractal dimensions of Weyl-Marchaud fractional derivative of certain one-dimensional functions. (English) Zbl 1434.26012 Fractals 27, No. 7, Article ID 1950114, 6 p. (2019). MSC: 26A33 PDFBibTeX XMLCite \textit{Y. S. Liang} and \textit{N. Liu}, Fractals 27, No. 7, Article ID 1950114, 6 p. (2019; Zbl 1434.26012) Full Text: DOI
Peng, Wen Liang; Yao, Kui; Zhang, Xia; Yao, Jia Box dimension of Weyl-Marchaud fractional derivative of linear fractal interpolation functions. (English) Zbl 1433.28025 Fractals 27, No. 4, Article ID 1950058, 6 p. (2019). MSC: 28A80 26A33 PDFBibTeX XMLCite \textit{W. L. Peng} et al., Fractals 27, No. 4, Article ID 1950058, 6 p. (2019; Zbl 1433.28025) Full Text: DOI
Djida, Jean-Daniel; Fernandez, Arran Interior regularity estimates for a degenerate elliptic equation with mixed boundary conditions. (English) Zbl 1432.35094 Axioms 7, No. 3, Paper No. 65, 16 p. (2018). MSC: 35J70 35B45 PDFBibTeX XMLCite \textit{J.-D. Djida} and \textit{A. Fernandez}, Axioms 7, No. 3, Paper No. 65, 16 p. (2018; Zbl 1432.35094) Full Text: DOI
Ferrari, Fausto Weyl and Marchaud derivatives: a forgotten history. (English) Zbl 1473.26006 Mathematics 6, No. 1, Paper No. 6, 25 p. (2018). MSC: 26A33 PDFBibTeX XMLCite \textit{F. Ferrari}, Mathematics 6, No. 1, Paper No. 6, 25 p. (2018; Zbl 1473.26006) Full Text: DOI arXiv
Kukushkin, M. V. On some qualitative properties of the operator of fractional differentiation in Kipriyanov sense. (Russian. English summary) Zbl 1392.26011 Vestn. Samar. Univ., Estestvennonauchn. Ser. 23, No. 2, 32-43 (2017). MSC: 26A33 26B99 PDFBibTeX XMLCite \textit{M. V. Kukushkin}, Vestn. Samar. Univ., Estestvennonauchn. Ser. 23, No. 2, 32--43 (2017; Zbl 1392.26011) Full Text: MNR
Mu, Lei; Yao, Kui; Qiu, Hua; Su, Weiyi The Hausdorff dimension of Weyl-Marchaud fractional derivative of a type of fractal functions. (Chinese. English summary) Zbl 1399.26012 Chin. Ann. Math., Ser. A 38, No. 3, 257-264 (2017). MSC: 26A33 28A78 28A80 PDFBibTeX XMLCite \textit{L. Mu} et al., Chin. Ann. Math., Ser. A 38, No. 3, 257--264 (2017; Zbl 1399.26012) Full Text: DOI
Bergounioux, Maïtine; Leaci, Antonio; Nardi, Giacomo; Tomarelli, Franco Fractional Sobolev spaces and functions of bounded variation of one variable. (English) Zbl 1371.26013 Fract. Calc. Appl. Anal. 20, No. 4, 936-962 (2017). MSC: 26A45 26A33 26A30 PDFBibTeX XMLCite \textit{M. Bergounioux} et al., Fract. Calc. Appl. Anal. 20, No. 4, 936--962 (2017; Zbl 1371.26013) Full Text: DOI arXiv
Allen, Mark; Caffarelli, Luis; Vasseur, Alexis Porous medium flow with both a fractional potential pressure and fractional time derivative. (English) Zbl 1372.35328 Chin. Ann. Math., Ser. B 38, No. 1, 45-82 (2017). MSC: 35R11 35K55 26A33 35D30 35B65 PDFBibTeX XMLCite \textit{M. Allen} et al., Chin. Ann. Math., Ser. B 38, No. 1, 45--82 (2017; Zbl 1372.35328) Full Text: DOI arXiv
Bucur, Claudia; Ferrari, Fausto An extension problem for the fractional derivative defined by Marchaud. (English) Zbl 1410.26014 Fract. Calc. Appl. Anal. 19, No. 4, 867-887 (2016). MSC: 26A33 34A08 35R11 45K05 35K65 PDFBibTeX XMLCite \textit{C. Bucur} and \textit{F. Ferrari}, Fract. Calc. Appl. Anal. 19, No. 4, 867--887 (2016; Zbl 1410.26014) Full Text: DOI arXiv
Samko, Stefan; Yakhshiboev, Mahmadyor U. A Chen-type modification of Hadamard fractional integro-differentiation. (English) Zbl 1318.26016 Bastos, M. Amélia (ed.) et al., Operator theory, operator algebras and applications. Selected papers based on the presentations at the workshop WOAT 2012, Lisbon, Portugal, September 11–14, 2012. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0815-6/hbk; 978-3-0348-0816-3/ebook). Operator Theory: Advances and Applications 242, 325-339 (2014). MSC: 26A33 PDFBibTeX XMLCite \textit{S. Samko} and \textit{M. U. Yakhshiboev}, Oper. Theory: Adv. Appl. 242, 325--339 (2014; Zbl 1318.26016) Full Text: DOI
Muratbekova, Moldir A.; Shinaliyev, Kanat M.; Turmetov, Batirkhan K. On solvability of a nonlocal problem for the Laplace equation with the fractional-order boundary operator. (English) Zbl 1304.35732 Bound. Value Probl. 2014, Paper No. 29, 13 p. (2014). MSC: 35R09 35R11 35J05 35J25 26A33 PDFBibTeX XMLCite \textit{M. A. Muratbekova} et al., Bound. Value Probl. 2014, Paper No. 29, 13 p. (2014; Zbl 1304.35732) Full Text: DOI
Bapna, I. B.; Mathur, Nisha Application of fractional calculus in statistics. (English) Zbl 1248.62028 Int. J. Contemp. Math. Sci. 7, No. 17-20, 849-856 (2012). MSC: 62F10 26A33 44A15 42B10 PDFBibTeX XMLCite \textit{I. B. Bapna} and \textit{N. Mathur}, Int. J. Contemp. Math. Sci. 7, No. 17--20, 849--856 (2012; Zbl 1248.62028) Full Text: Link
Zhang, Qi; Liang, Yongshun The Weyl-Marchaud fractional derivative of a type of self-affine functions. (English) Zbl 1250.26008 Appl. Math. Comput. 218, No. 17, 8695-8701 (2012). MSC: 26A33 28A80 PDFBibTeX XMLCite \textit{Q. Zhang} and \textit{Y. Liang}, Appl. Math. Comput. 218, No. 17, 8695--8701 (2012; Zbl 1250.26008) Full Text: DOI
Babenko, V. F.; Pichugov, S. A. Sharp estimates of the norms of fractional derivatives of functions of several variables satisfying Hölder conditions. (English. Russian original) Zbl 1205.26008 Math. Notes 87, No. 1, 23-30 (2010); translation from Mat. Zametki 87, No. 1, 26-34 (2010). Reviewer: Juan J. Trujillo (La Laguna) MSC: 26A33 26D10 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{S. A. Pichugov}, Math. Notes 87, No. 1, 23--30 (2010; Zbl 1205.26008); translation from Mat. Zametki 87, No. 1, 26--34 (2010) Full Text: DOI
Carpinteri, Alberto; Cornetti, Pietro; Sapora, Alberto Static-kinematic fractional operators for fractal and non-local solids. (English) Zbl 1159.74001 ZAMM, Z. Angew. Math. Mech. 89, No. 3, 207-217 (2009). MSC: 74A99 26A33 28A80 PDFBibTeX XMLCite \textit{A. Carpinteri} et al., ZAMM, Z. Angew. Math. Mech. 89, No. 3, 207--217 (2009; Zbl 1159.74001) Full Text: DOI
Rafeiro, Humberto; Samko, Stefan Characterization of the range of one-dimensional fractional integration in the space with variable exponent. (English) Zbl 1160.46022 Bastos, Maria Amélia (ed.) et al., Operator algebras, operator theory and applications. Selected papers of the international summer school and workshop, WOAT 2006, Lisbon, Portugal, September 1–5, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8683-2/hbk). Operator Theory: Advances and Applications 181, 393-416 (2008). MSC: 46E30 47B38 26A33 PDFBibTeX XMLCite \textit{H. Rafeiro} and \textit{S. Samko}, Oper. Theory: Adv. Appl. 181, 393--416 (2008; Zbl 1160.46022)
Rafeiro, Humberto; Samko, Stefan On multidimensional analogue of Marchaud formula for fractional Riesz-type derivatives in domains in \(\mathbb R^n\). (English) Zbl 1141.42014 Fract. Calc. Appl. Anal. 8, No. 4, 393-401 (2005). Reviewer: Zhibo Lu (Zhengzhou) MSC: 42B20 26A33 PDFBibTeX XMLCite \textit{H. Rafeiro} and \textit{S. Samko}, Fract. Calc. Appl. Anal. 8, No. 4, 393--401 (2005; Zbl 1141.42014) Full Text: EuDML
Il’chenko, S. A. Comparison of properties of the Liouville and Marchaud fractional derivatives of functions of several variables. (Ukrainian. English summary) Zbl 1064.60119 Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 2003, No. 9, 41-48 (2003). MSC: 60H05 PDFBibTeX XMLCite \textit{S. A. Il'chenko}, Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 2003, No. 9, 41--48 (2003; Zbl 1064.60119)
Samko, Natalia G.; Samko, Stefan G. On approximative definition of fractional differentiation. (English) Zbl 1030.26008 Fract. Calc. Appl. Anal. 2, No. 3, 329-342 (1999). MSC: 26A33 PDFBibTeX XMLCite \textit{N. G. Samko} and \textit{S. G. Samko}, Fract. Calc. Appl. Anal. 2, No. 3, 329--342 (1999; Zbl 1030.26008)
Zähle, M. Fractional differentiation in the self-affine case. V: The local degree of differentiability. (English) Zbl 1016.26009 Math. Nachr. 185, 279-306 (1997). Reviewer: Lars Olsen (MR 99a:26007) MSC: 26A33 28A80 60G18 60G57 PDFBibTeX XMLCite \textit{M. Zähle}, Math. Nachr. 185, 279--306 (1997; Zbl 1016.26009) Full Text: DOI
Samko, S. G. Fractional integration and differentiation of variable order. (English) Zbl 0838.26006 Anal. Math. 21, No. 3, 213-236 (1995). Reviewer: A.A.Kilbas (Minsk) MSC: 26A33 45P05 47B38 PDFBibTeX XMLCite \textit{S. G. Samko}, Anal. Math. 21, No. 3, 213--236 (1995; Zbl 0838.26006) Full Text: DOI
Samko, S. G. Fractional differentiation and integration of variable order. (English. Russian original) Zbl 0886.26006 Dokl. Math. 51, No. 3, 401-403 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 342, No. 4, 458-460 (1995). Reviewer: A.A.Kilbas (Minsk) MSC: 26A33 45P05 47B38 PDFBibTeX XMLCite \textit{S. G. Samko}, Dokl. Math. 51, No. 3, 401--403 (1995; Zbl 0886.26006); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 342, No. 4, 458--460 (1995)
Samko, Stefan G.; Ross, Bertram Integration and differentiation to a variable fractional order. (English) Zbl 0820.26003 Integral Transforms Spec. Funct. 1, No. 4, 277-300 (1993). MSC: 26A33 31B10 42A38 PDFBibTeX XMLCite \textit{S. G. Samko} and \textit{B. Ross}, Integral Transforms Spec. Funct. 1, No. 4, 277--300 (1993; Zbl 0820.26003) Full Text: DOI
Grin’ko, A. P. Operators of generalized integrodifferentiation of fractional order with Gauss hypergeometric function in the kernel. (Russian) Zbl 0819.47066 Dokl. Akad. Nauk Belarusi 37, No. 3, 26-29 (1993). Reviewer: C.Constanda (Glasgow) MSC: 47G20 PDFBibTeX XMLCite \textit{A. P. Grin'ko}, Dokl. Akad. Nauk Belarusi 37, No. 3, 26--29 (1993; Zbl 0819.47066)
Dobrushkin, V. A. Regularization in Marchaud’s form and approximate evaluation of a class of integral-differential expressions. (English. Russian original) Zbl 0802.65138 Russ. Math. 36, No. 9, 34-37 (1992); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1992, No. 9 (364), 38-41 (1992). MSC: 65R20 65D25 45K05 PDFBibTeX XMLCite \textit{V. A. Dobrushkin}, Russ. Math. 36, No. 9, 38--41 (1992; Zbl 0802.65138); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1992, No. 9 (364), 38--41 (1992)
Shakh, L. G. On an approximate continuity condition for the fractional derivative. (English. Russian original) Zbl 0786.41029 Ukr. Math. J. 44, No. 12, 1575-1578 (1992); translation from Ukr. Mat. Zh. 44, No. 12, 1719-1722 (1992). MSC: 41A65 PDFBibTeX XMLCite \textit{L. G. Shakh}, Ukr. Mat. Zh. 44, No. 12, 1719--1722 (1992; Zbl 0786.41029); translation from Ukr. Mat. Zh. 44, No. 12, 1719--1722 (1992) Full Text: DOI
Rubin, B. S. Analogies to the Marchaud derivative for convolutions with power- logarithmic kernels on a finite segment. (Russian) Zbl 0773.26003 Mathematical analysis and its applications, 133-139 (1992). Reviewer: A.I.Khejfits (Rostov-na-Donu) MSC: 26A33 44A35 PDFBibTeX XMLCite \textit{B. S. Rubin}, in: Mathematical analysis and its applications, . 133--139 (1992; Zbl 0773.26003)