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AIMS Mathematics

2023, Volume 8, Issue 3: 7377-7393. doi: 10.3934/math.2023371
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Existence and uniqueness results for mixed derivative involving fractional operators

  • 1.
    Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia
  • 2.
    Department of Mathematics and Statistics, University of Lahore, Sargodha, Pakistan
  • 3.
    Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
  • Received: 12 November 2022 Revised: 05 January 2023 Accepted: 09 January 2023 Published: 16 January 2023

  • MSC : 34K37, 47A10, 49J15

  • In this article, we discuss the existence and uniqueness results for mix derivative involving fractional operators of order $ \beta\in (1, 2) $ and $ \gamma\in (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.

    Citation: Abeer Al Elaiw, Farva Hafeez, Mdi Begum Jeelani, Muath Awadalla, Kinda Abuasbeh. Existence and uniqueness results for mixed derivative involving fractional operators[J]. AIMS Mathematics, 2023, 8(3): 7377-7393. doi: 10.3934/math.2023371

    Related Papers:

  • In this article, we discuss the existence and uniqueness results for mix derivative involving fractional operators of order $ \beta\in (1, 2) $ and $ \gamma\in (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.


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