Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 13 2 2022 07 16 Mixed nonlocal boundary value problem for implicit fractional differential equation involving both retarded and advanced arguments 2697 2708 6746 10.22075/ijnaa.2022.26751.3403 EN Nedjemeddine Derdar Department of Mathematics, Higher Normal School of Technological Education- Skikda, Algeria Journal Article 2022 04 09 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<br />given to illustrate the results. Hilfer–Hadamard fractional derivative Implicit fractional differential equations retarded argument advanced argument fixed point theorems existence and uniqueness https://ijnaa.semnan.ac.ir/article_6746_88aba5d864785cd8be9b02d824d5ef99.pdf