Nonlinear Degenerate Fractional Evolution Equations with Nonlocal Conditions

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Derdar, Nedjemeddine^a | Debbouche, Amar^{b; *}

Affiliations: [a] Laboratory of Mathematics, Department of Mathematics, University of Badji, Mokhtar 23000, Annaba, Algeria | [b] Department of Mathematics, Guelma University, Guelma 24000, Algeria. amar_debbouche@yahoo.fr

Correspondence: [*] Address for correspondence: Department of Mathematics, Guelma University, Guelma 24000, Algeria

Abstract: We investigate the unique solvability of a class of nonlinear nonlocal differential equations associated with degenerate linear operator at the fractional Caputo derivative. For the main results, we use the theory of fractional calculus and (L, p)-boundedness technique that based on the analysis of both strongly (L, p)-sectorial operators and strongly (L, p)-radial operators. The obtained results are applicable to degenerate fractional Cauchy and Showalter–Sidorov problems in Banach spaces. Finally, we give an application described by time-fractional order Oskolkov system.

Keywords: Degenerate nonlinear equation, fractional calculus, (L, p)-bounded operator, non-local condition

DOI: 10.3233/FI-2017-1505

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 473-485, 2017