On perturbations of abstract fractional differential equations by nonlinear operators
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We prove the unique solvability of a Cauchy-type problem for an abstract parabolic equation containing fractional derivatives and a nonlinear perturbation term. The result is applied to establish the solvability of the inverse coefficient problem for a fractional-order equation.
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- 2.M. M. Dzhrbashyan, Integral Transformations and the Presentation of Functions in a Complex Domain [in Russian], Nauka, Moscow (1966).Google Scholar
- 4.A. V. Glushak, “On the Cauchy-type problem for abstract fractional-order differential equations,” Vestnik Voronezh. Univ. Ser. Fiz. Mat., No. 2, 74–77 (2001).Google Scholar
- 5.A. V. Glushak and H. K. Avad, “On perturbations of abstract fractional differential equations,” Dokl. Adyg (Cherkes) Int. Akad. Nauk, 10, No. 1, 25–31 (2008).Google Scholar
- 6.A. V. Glushak and Yu.V. Povalyaeva, “On properties of solutions of Cauchy-type problems for abstract fractional differential equations,” Spectral and Evolution Problems, 14, 163–172 (2004).Google Scholar
- 7.K. Iosida, Functional Analysis [Russian translation], Mir, Moscow (1967).Google Scholar
- 9.A. A. Kilbas, H.M. Srivastava, and J. J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier Science B.V., Amsterdam (2006).Google Scholar
- 16.A. V. Pskhu, Boundary-Value Problems for Fractional-Order and Continual-Order Partial Differential Equations [in Russian], Kabardino-Balkar Scientific Center, Nal’chik (2005).Google Scholar
- 18.S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications [in Russian], Nauka i Tekhnika, Minsk (1987).Google Scholar