Abstract
In the paper, we study a boundary value problem for a class of ψ-Hilfer fractional-order Langevin equations with multi-point integral boundary conditions. Existence and uniqueness results are established by using well-known fixed point theorems. Examples illustrating the main results are also included.
Highlights
Fractional differential equations are important since their nonlocal property is suitable to characterize memory phenomena in economic, control, and material sciences
The study of a boundary value problem for fractional-order ψ-Hilfer fractional derivative (HFD) was done by Harikrishnan et al [21]
There has been published some significant work about the nonlinear boundary value problems for HFD, out of which we mention only a few that are relating to this article; see [22,23,24]
Summary
Fractional differential equations are important since their nonlocal property is suitable to characterize memory phenomena in economic, control, and material sciences. Asawasamrit et al [19] studied the nonlocal boundary value problems for fractional-order differential equations with HFD subject to nonlocal integral boundary conditions. In [20], Saengthong et al considered the existence results for Hilfer–Hadamard sequential fractional differential equations with two point boundary conditions. The study of a boundary value problem for fractional-order ψ-HFD was done by Harikrishnan et al [21].
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