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Well Posedness
and Stability
for the
Nonlinear
φ-Caputo Hybrid
Fractional
Boundary Value
Problems with
Two-Point Hybrid
Boundary
Conditions
Yahia Awad
Department of
Mathematics and
Physics,
Lebanese
International
University
(LIU), Bekaa
Campus, Lebanon
Email address:
yehya.awad@liu.edu.lb
ORCID: https://orcid.org/0000-0001-9878-2482
Doi :
https://doi.org/10.47013/16.4.2
Cited by :
Jordan J. Math &
Stat.,
16 (4) (2023),
617 - 647
PDF
Received on:
Aug. 28,
2022;
Accepted
on: March 26,
2023
Abstract. This article
investigates
into the study
of nonlinear
hybrid
fractional
boundary value
problems, which
involve ϕ-Caputo
derivatives of
fractional order
and two-point
hybrid boundary
conditions. The
author utilizes
a fixed point
theorem of Dhage
to provide
evidence for the
existence and
uniqueness of
solutions,
taking into
consideration
mixed Lipschitz
and Caratheodory
conditions.
Additionally,
the Ulam-Hyers
types of
stability are
established in
this context.
The article
concludes by
introducing a
class of
fractional
boundary value
problems, which
are dependent on
the arbitrary
values of ϕ and
the boundary
conditions
chosen. The
research
presented in
this article has
the potential to
be useful in
various fields,
such as
engineering and
science, where
fractional
differential
equations are
frequently used
to model complex
phenomena.
Keywords: Hybrid
fractional
differential
equation,
Boundary value
problem, Green’s
function, Dhage
fixed point
theorem,
ϕ-Caputo
fractional
derivatives,
Existence
Results,
Hyers-Ulam
stability of
solutions.
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