Existence and uniqueness of nonlocal boundary conditions for Hilfer–Hadamard-type fractional differential equations

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 1 - 20
• Main Authors: Salamooni, Ahmad Y. A., Pawar, D. D.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 07-04-2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Banach spaces; Boundary conditions; Difference and Functional Equations; Differential equations; Existence; Existence theorems; Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations; Fixed points (mathematics); Fractional differential equation and fractional calculus; Functional Analysis; Hilfer–Hadamard type; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinear boundary value problems; Ordinary Differential Equations; Partial Differential Equations; Uniqueness; Uniqueness; 35R11; Nonlinear boundary value problems; Hilfer–Hadamard type; Fractional differential equation and fractional calculus; Existence; 34A08
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-021-03358-0

In this paper, we use some fixed point theorems in Banach space for studying the existence and uniqueness results for Hilfer–Hadamard-type fractional differential equations
D
α
,
β
H
x
(
t
)
+
f
(
t
,
x
(
t
)
)
=
0
on the interval
(
1
,
e
]
with nonlinear boundary conditions
x
(
1
+
ϵ
)
=
∑
i
=
1
n
−
2
ν
i
x
(
ζ
i
)
,
H
D
1
,
1
x
(
e
)
=
∑
i
=
1
n
−
2
σ
i
H
D
1
,
1
x
(
ζ
i
)
.