Abstract
In this paper we study the global solvability of several ordinary and partial fractional integro-differential equations in theWiener space of functions with bounded square averages.
MSC 2010: Primary: 44A10, 26A33, 45K05; Secondary: 35D35, 35R30
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Akilandeeswari, K. Balachandran, and N. Annapoorani, On fractional partial differential equations of diffusion type with integral kernel. In: Mathematical Modelling, Optimization, Analytic and Numerical Solutions, Eds: P. Manchanda, R.P. Lozi, and A.H. Siddiqi, Springer, Singapore, 2020, 333–349.
Sh.A. Alimov, V.A. Ilyin, and E.M. Nikishin, Convergence problems of multiple Fourier series and spectral decompositions, II (In Russian). Uspekhi Mat. Nauk 32 (1977), 107–130; Engl. transl. in: Russian Math. Surveys 32 (1977), 115–139.
R.L. Bagley and P.J. Torvik, Fractional calculus, a different approach to the analysis of viscoelastically damped structures. AIAA J. 21 (1983), 741–748.
R.L. Bagley and P.J. Torvik, On the fractional calculus model of viscoelastic behavior, J. Rheol. 30 (1986), 133–155.
M.Sh. Birman and M.Z. Solomyak, The principal term of the spectral asymptotics for non-smooth elliptic problems (In Russian). Funktsional. Anal. i Prilozhen. 4, No 4 (1970), 1–13; Engl. transl. in Functional Analysis Appl. 4 (1971), 265–275.
M.Sh. Birman and M.Z. Solomyak, Spectral asymptotics of nonsmooth elliptic operators, I (In Russian). Trudy Moskov. Mat. Obshch. 27 (1972), 3–52; Engl. transl. in Trans. Moscow Math. Soc. 27 (1972/1975), 1–52.
M.M. El-Borai and A. Debbouche, On some fractional integro-differential equations with analytic semigroups. Intern. J. of Contemp. Math. Sci. 4, No 25-28 (2009), 1361–1371.
R. Gorenflo, A.A. Kilbas, F. Mainardi, and S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications. Springer, Berlin, 2014.
A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Math. Studies, Vol. 204, Elsevier, New York, 2006.
V.P. Mikhailov, Partial Differential Equations. Mir, Moscow, 1978.
R.E.A.C. Paley and N. Wiener, Fourier Transforms in the Complex Domain. Amer. Math. Soc. Coll. Publ. 19, 1934.
Y.A. Rossikhin and M.V. Shitikova, Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 50 (1997), 15–67.
F. Saedpanah, Existence and Uniqueness of the Solution of an Integro-Differential Equation with Weakly Singular Kernel. Dept. of Math. Sciences, Chalmers University of Technology, 2009.
Vu Kim Tuan, Laplace transform of functions with bounded averages. Intern. J. of Evolution Equations 1, No 4 (2005), 429–433.
Vu Kim Tuan, Inverse problem for fractional diffusion equation. Fract. Calc. Appl. Anal. 14, No 1 (2011), 31–55; DOI: 10.2478/s13540-011-0004-x; https://www.degruyter.com/view/journals/fca/14/1/fca.14.issue-1.xml
D.V. Widder, The Laplace Transform. Princeton Univ. Press, Princeton, 1946.
N. Wiener, Generalized harmonic analysis. Acta Math. 55 (1930), 117–258.
H. Ye, J. Gao, and Y. Ding, A generalized Gronwall inequality and its application to a fractional differential equation. J. Math. Anal. Appl. 328 (2007), 1075–1081.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Tuan, V.K. Fractional Integro-Differential Equations in Wiener Spaces. Fract Calc Appl Anal 23, 1300–1328 (2020). https://doi.org/10.1515/fca-2020-0065
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1515/fca-2020-0065