Mixed nonlocal boundary value problem for implicit fractional differential equation involving both retarded and advanced arguments

	Mixed nonlocal boundary value problem for implicit fractional differential equation involving both retarded and advanced arguments
International Journal of Nonlinear Analysis and Applications
مقاله 217، دوره 13، شماره 2، مهر 2022، صفحه 2697-2708 اصل مقاله (390.26 K)
نوع مقاله: Review articles
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.26751.3403
نویسنده
Nedjemeddine Derdar^*
Department of Mathematics, Higher Normal School of Technological Education- Skikda, Algeria
چکیده
In this paper, we investigate the existence and uniqueness of solutions for nonlinear implicit Hilfer-Hadamard fractional differential equations involving both retarded and advanced arguments and nonlocal mixed boundary conditions. We also use the Banach contraction mapping principle and Schaefer’s fixed point theorem to show the existence and uniqueness of solutions. The results obtained here extend the work of Benchohra et al. [10] and Haoues et al. [18]. An example is also given to illustrate the results.
کلیدواژه‌ها
Hilfer–Hadamard fractional derivative؛ Implicit fractional differential equations؛ retarded argument؛ advanced argument؛ Fixed point theorems؛ Existence and uniqueness
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