Existence of solutions of multi-order fractional differential equations

Faycal Bouchelaghem; Hamid Boulares; Abdelouaheb Ardjouni; Fahd Jarad; Thabet Abdeljawad; Bahaaeldin Abdalla; Kamal Shah

doi:10.1016/j.padiff.2025.101104

Existence of solutions of multi-order fractional differential equations

Faycal Bouchelaghem, Hamid Boulares, Abdelouaheb Ardjouni, Fahd Jarad, Thabet Abdeljawad^*, Bahaaeldin Abdalla, Kamal Shah

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings.

Original language	English
Article number	101104
Journal	Partial Differential Equations in Applied Mathematics
Volume	13
DOIs	https://doi.org/10.1016/j.padiff.2025.101104
Publication status	Published - Mar 2025
Externally published	Yes

Keywords

Banach fixed point theorems
Existence
Multi-order
Riemann–Liouville fractional derivatives
Uniqueness

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10.1016/j.padiff.2025.101104

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title = "Existence of solutions of multi-order fractional differential equations",

abstract = "Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings.",

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author = "Faycal Bouchelaghem and Hamid Boulares and Abdelouaheb Ardjouni and Fahd Jarad and Thabet Abdeljawad and Bahaaeldin Abdalla and Kamal Shah",

note = "Publisher Copyright: {\textcopyright} 2025",

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doi = "10.1016/j.padiff.2025.101104",

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T1 - Existence of solutions of multi-order fractional differential equations

AU - Bouchelaghem, Faycal

AU - Boulares, Hamid

AU - Ardjouni, Abdelouaheb

AU - Jarad, Fahd

AU - Abdeljawad, Thabet

AU - Abdalla, Bahaaeldin

AU - Shah, Kamal

PY - 2025/3

Y1 - 2025/3

N2 - Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings.

AB - Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings.

KW - Banach fixed point theorems

KW - Existence

KW - Multi-order

KW - Riemann–Liouville fractional derivatives

KW - Uniqueness

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DO - 10.1016/j.padiff.2025.101104

M3 - Article

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SN - 2666-8181

VL - 13

JO - Partial Differential Equations in Applied Mathematics

JF - Partial Differential Equations in Applied Mathematics

M1 - 101104

ER -

Existence of solutions of multi-order fractional differential equations

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Keywords

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