DOI: 10.24193/fpt-ro.2023.1.01

Authors: Bashir Ahmad, Sotiris K. Ntouyas and Fawziah M. Alotaibi

Abstract: We study a novel fractional model of boundary value problems in the setting of Hilfer fractional derivative operators. Precisely, sequential Hilfer fractional differential equations and inclusions with integro-multistrip-multi-point boundary conditions are considered. Existence and uniqueness results are established for the proposed problems by using the techniques of fixed point theory. In the single-valued case, the classical theorems due to Banach and Krasnosel'skiĭ are used, while the multi-valued case is investigated with the aid of Leray-Schauder nonlinear alternative for multi-valued maps, and Covitz and Nadler's fixed point theorem for multi-valued contractions. The obtained results are well-illustrated by numerical examples.

Key Words and Phrases: Fractional differential equation and inclusion, boundary value problem, fractional derivative, fractional integral, fixed point theorem, multi-valued map.

2010 Mathematics Subject Classification: 26A33, 34A60, 34B15, 47H10.

Published on-line: February 1st, 2023.

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