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Research Article | Open Access

Existence and uniqueness results for mixed derivative involving fractional operators

Abeer Al Elaiw1, Farva Hafeez2, Mdi Begum Jeelani3( ), Muath Awadalla1( ), Kinda Abuasbeh1
Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia
Department of Mathematics and Statistics, University of Lahore, Sargodha, Pakistan
Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
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Abstract

In this article, we discuss the existence and uniqueness results for mix derivative involving fractional operators of order β ∈ ( 1 , 2 ) and γ ∈ ( 0 , 1 ). We prove some important results by using integro-differential equation of pantograph type. We establish the existence and uniqueness of the solutions using fixed point theorem. Furthermore, one application is likewise given to represent our fundamental results.

Keywords

fractional derivativesexistence conditionsintegro-differential equationspantograph equations
CLC number: 34K37, 47A10, 49J15

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 7377-7393
DOI: 10.3934/math.2023371

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Cite this article:
Al Elaiw A, Hafeez F, Jeelani MB, et al. Existence and uniqueness results for mixed derivative involving fractional operators. AIMS Mathematics, 2023, 8(3): 7377-7393. https://doi.org/10.3934/math.2023371

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Received: 12 November 2022
Revised: 05 January 2023
Accepted: 09 January 2023
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)