The Existence and Stability of Integral Fractional Differential Equations

The main goal of this research is to study integro-fractional differential equations and simulate their dynamic behavior using ABC-fractional derivatives. We investigate the Hyers–Ulam stability of the proposed system and further expand the prerequisites for the existence and uniqueness of the solut...

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Main Authors: Rahman Ullah Khan, Ioan-Lucian Popa
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Fractal and Fractional
Subjects:
Online Access:https://www.mdpi.com/2504-3110/9/5/295
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author Rahman Ullah Khan
Ioan-Lucian Popa
author_facet Rahman Ullah Khan
Ioan-Lucian Popa
author_sort Rahman Ullah Khan
collection DOAJ
description The main goal of this research is to study integro-fractional differential equations and simulate their dynamic behavior using ABC-fractional derivatives. We investigate the Hyers–Ulam stability of the proposed system and further expand the prerequisites for the existence and uniqueness of the solutions. The Schauder fixed-point theorem and the Banach contraction principle are employed to obtain the results. Finally, we present an example to demonstrate the practical application of our theoretical conclusions.
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spelling doaj-art-eabe6de967e04dc6bcfd30f52aed39122025-08-20T03:47:59ZengMDPI AGFractal and Fractional2504-31102025-05-019529510.3390/fractalfract9050295The Existence and Stability of Integral Fractional Differential EquationsRahman Ullah Khan0Ioan-Lucian Popa1Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, RomaniaThe main goal of this research is to study integro-fractional differential equations and simulate their dynamic behavior using ABC-fractional derivatives. We investigate the Hyers–Ulam stability of the proposed system and further expand the prerequisites for the existence and uniqueness of the solutions. The Schauder fixed-point theorem and the Banach contraction principle are employed to obtain the results. Finally, we present an example to demonstrate the practical application of our theoretical conclusions.https://www.mdpi.com/2504-3110/9/5/295integral fractional differential equationABC-fractional derivativefixed-point theoremsstability
spellingShingle Rahman Ullah Khan
Ioan-Lucian Popa
The Existence and Stability of Integral Fractional Differential Equations
Fractal and Fractional
integral fractional differential equation
ABC-fractional derivative
fixed-point theorems
stability
title The Existence and Stability of Integral Fractional Differential Equations
title_full The Existence and Stability of Integral Fractional Differential Equations
title_fullStr The Existence and Stability of Integral Fractional Differential Equations
title_full_unstemmed The Existence and Stability of Integral Fractional Differential Equations
title_short The Existence and Stability of Integral Fractional Differential Equations
title_sort existence and stability of integral fractional differential equations
topic integral fractional differential equation
ABC-fractional derivative
fixed-point theorems
stability
url https://www.mdpi.com/2504-3110/9/5/295
work_keys_str_mv AT rahmanullahkhan theexistenceandstabilityofintegralfractionaldifferentialequations
AT ioanlucianpopa theexistenceandstabilityofintegralfractionaldifferentialequations
AT rahmanullahkhan existenceandstabilityofintegralfractionaldifferentialequations
AT ioanlucianpopa existenceandstabilityofintegralfractionaldifferentialequations