Implicit Hybrid Fractional Boundary Value Problem via Generalized Hilfer Derivative

Abstract

This research paper is dedicated to the study of a class of boundary value problems for a nonlinear, implicit, hybrid, fractional, differential equation, supplemented with boundary conditions involving general fractional derivatives, known as the ϑ-Hilfer and ϑ-Riemann–Liouville fractional operators. The existence of solutions to the mentioned problem is obtained by some auxiliary conditions and applied Dhage’s fixed point theorem on Banach algebras. The considered problem covers some symmetry cases, with respect to a ϑ function. Moreover, we present a pertinent example to corroborate the reported results.

Keywords

• ϑ-Hilfer fractional operator
• implicit
• Dhage fixed point theorem
• Banach algebras