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Existence and uniqueness of neutral functional differential equations with sequential fractional operators.

ABSTRACT: In this research paper, we investigate the existence and uniqueness of solutions for neutral functional differential equations with sequential fractional orders, specifically involving the [Formula: see text]-Caputo operator. To obtain the desired results, we employ the Banach fixed point theorem (BFPT), a nonlinear variation of the Leray-Schauder fixed point theorem (SFPT), and the Krasnoselski fixed point theorem (KFPT). Additionally, we provide illustrative examples that demonstrate the key findings. Furthermore, we address a scenario where an initial value integral condition is considered.

SUBMITTER: Debbar R

PROVIDER: S-EPMC11251599 | biostudies-literature | 2024

REPOSITORIES: biostudies-literature

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Existence and uniqueness of neutral functional differential equations with sequential fractional operators.

Debbar Rabah R Boulares Hamid H Moumen Abdelkader A Alraqad Tariq T Saber Hicham H

PloS one 20240716 7

In this research paper, we investigate the existence and uniqueness of solutions for neutral functional differential equations with sequential fractional orders, specifically involving the [Formula: see text]-Caputo operator. To obtain the desired results, we employ the Banach fixed point theorem (BFPT), a nonlinear variation of the Leray-Schauder fixed point theorem (SFPT), and the Krasnoselski fixed point theorem (KFPT). Additionally, we provide illustrative examples that demonstrate the key f ...[more]

PMID: 39012860

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