Analysis study on multi-order ϱ-Hilfer fractional pantograph implicit differential equation on unbounded domains

Sabri T.M. Thabet; Sa’Ud Al-Sa’di; Imed Kedim; Ava Sh Rafeeq; Shahram Rezapour

doi:10.3934/math.2023938

Analysis study on multi-order ϱ-Hilfer fractional pantograph implicit differential equation on unbounded domains

Sabri T.M. Thabet, Sa’Ud Al-Sa’di, Imed Kedim, Ava Sh Rafeeq, Shahram Rezapour

Mathematics

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

24 Scopus citations

Abstract

In this paper, we investigate a multi-order ϱ-Hilfer fractional pantograph implicit differential equation on unbounded domains (a, ∞), a ≥ 0. The existence and uniqueness of solution are established for a such problem by utilizing the Banach fixed point theorem in an applicable Banach space. In addition, stability of the types Ulam-Hyers (UH), Ulam-Hyers-Rassias (UHR) and semi-Ulam-Hyers-Rassias (s-UHR) are discussed by using nonlinear analysis topics. Finally, a concrete example includes some particular cases is enhanced to illustrate rightful of our results.

Original language	English
Pages (from-to)	18455-18473
Number of pages	19
Journal	AIMS Mathematics
Volume	8
Issue number	8
DOIs	https://doi.org/10.3934/math.2023938
State	Published - 2023

Keywords

Ulam-Hyers-Rassias stability
fixed point theorems
multi-order
pantograph implicit differential equations
ϱ-Hilfer fractional derivatives

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10.3934/math.2023938

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title = "Analysis study on multi-order ϱ-Hilfer fractional pantograph implicit differential equation on unbounded domains",

abstract = "In this paper, we investigate a multi-order ϱ-Hilfer fractional pantograph implicit differential equation on unbounded domains (a, ∞), a ≥ 0. The existence and uniqueness of solution are established for a such problem by utilizing the Banach fixed point theorem in an applicable Banach space. In addition, stability of the types Ulam-Hyers (UH), Ulam-Hyers-Rassias (UHR) and semi-Ulam-Hyers-Rassias (s-UHR) are discussed by using nonlinear analysis topics. Finally, a concrete example includes some particular cases is enhanced to illustrate rightful of our results.",

keywords = "Ulam-Hyers-Rassias stability, fixed point theorems, multi-order, pantograph implicit differential equations, ϱ-Hilfer fractional derivatives",

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AU - Thabet, Sabri T.M.

AU - Al-Sa’di, Sa’Ud

AU - Kedim, Imed

AU - Rafeeq, Ava Sh

AU - Rezapour, Shahram

PY - 2023

Y1 - 2023

N2 - In this paper, we investigate a multi-order ϱ-Hilfer fractional pantograph implicit differential equation on unbounded domains (a, ∞), a ≥ 0. The existence and uniqueness of solution are established for a such problem by utilizing the Banach fixed point theorem in an applicable Banach space. In addition, stability of the types Ulam-Hyers (UH), Ulam-Hyers-Rassias (UHR) and semi-Ulam-Hyers-Rassias (s-UHR) are discussed by using nonlinear analysis topics. Finally, a concrete example includes some particular cases is enhanced to illustrate rightful of our results.

AB - In this paper, we investigate a multi-order ϱ-Hilfer fractional pantograph implicit differential equation on unbounded domains (a, ∞), a ≥ 0. The existence and uniqueness of solution are established for a such problem by utilizing the Banach fixed point theorem in an applicable Banach space. In addition, stability of the types Ulam-Hyers (UH), Ulam-Hyers-Rassias (UHR) and semi-Ulam-Hyers-Rassias (s-UHR) are discussed by using nonlinear analysis topics. Finally, a concrete example includes some particular cases is enhanced to illustrate rightful of our results.

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KW - fixed point theorems

KW - multi-order

KW - pantograph implicit differential equations

KW - ϱ-Hilfer fractional derivatives

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Analysis study on multi-order ϱ-Hilfer fractional pantograph implicit differential equation on unbounded domains

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