Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach

Muhammad Yaseen; Sadia Mumtaz; Reny George; Azhar Hussain

doi:10.3390/fractalfract6010017

Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach

Muhammad Yaseen
, Sadia Mumtaz
, Reny George
, Azhar Hussain

Mathematics

University of Sargodha

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

2 Scopus citations

Abstract

In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.

Original language	English
Article number	17
Journal	Fractal and Fractional
Volume	6
Issue number	1
DOIs	https://doi.org/10.3390/fractalfract6010017
State	Published - Jan 2022

Keywords

Caputo-Hadamard fractional derivative
Caputo-Hadamard fractional integral
Hybrid Caputo-Hadamard fractional differential equation and inclusion
Thermostat modeling

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10.3390/fractalfract6010017

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title = "Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage{\textquoteright}s Approach",

abstract = "In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.",

keywords = "Caputo-Hadamard fractional derivative, Caputo-Hadamard fractional integral, Hybrid Caputo-Hadamard fractional differential equation and inclusion, Thermostat modeling",

author = "Muhammad Yaseen and Sadia Mumtaz and Reny George and Azhar Hussain",

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T1 - Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach

AU - Yaseen, Muhammad

AU - Mumtaz, Sadia

AU - George, Reny

AU - Hussain, Azhar

PY - 2022/1

Y1 - 2022/1

N2 - In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.

AB - In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.

KW - Caputo-Hadamard fractional derivative

KW - Caputo-Hadamard fractional integral

KW - Hybrid Caputo-Hadamard fractional differential equation and inclusion

KW - Thermostat modeling

UR - https://www.scopus.com/pages/publications/85123793503

U2 - 10.3390/fractalfract6010017

DO - 10.3390/fractalfract6010017

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SN - 2504-3110

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JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 1

M1 - 17

ER -

Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach

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Keywords

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