Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions

Saleh S. Redhwan; Sadikali L. Shaikh; Mohammed S. Abdo; Wasfi Shatanawi; Kamaleldin Abodayeh; Mohammed A. Almalahi; Tariq Aljaaidi; Saleh S. Redhwan; Sadikali L. Shaikh; Mohammed S. Abdo; Wasfi Shatanawi; Kamaleldin Abodayeh; Mohammed A. Almalahi; Tariq Aljaaidi

doi:10.3934/math.2022107

AIMS Mathematics

2022, Volume 7, Issue 2: 1856-1872. doi: 10.3934/math.2022107

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Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions

1.
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, 431001 (M.S.), India
2.
Department of Mathematics, Maulana Azad College of arts, Science and Commerce, RozaBagh, Aurangabad 431004 (M.S.), India
3.
Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen
4.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
6.
Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan
7.
Department of Mathematics, Hajjah University, Hajjah, Yemen

Received: 25 August 2021 Accepted: 24 October 2021 Published: 03 November 2021
MSC : 34A08, 34A12, 34B15, 47H10

In this paper, we investigate a nonlinear generalized fractional differential equation with two-point and integral boundary conditions in the frame of $ \kappa $-Hilfer fractional derivative. The existence and uniqueness results are obtained using Krasnoselskii and Banach's fixed point theorems. We analyze different types of stability results of the proposed problem by using some mathematical methodologies. At the end of the paper, we present a numerical example to demonstrate and validate our findings.
- $ \kappa $-Hilfer fractional derivative,
- boundary conditions,
- fixed point theorem
Citation: Saleh S. Redhwan, Sadikali L. Shaikh, Mohammed S. Abdo, Wasfi Shatanawi, Kamaleldin Abodayeh, Mohammed A. Almalahi, Tariq Aljaaidi. Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions[J]. AIMS Mathematics, 2022, 7(2): 1856-1872. doi: 10.3934/math.2022107

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Abstract

In this paper, we investigate a nonlinear generalized fractional differential equation with two-point and integral boundary conditions in the frame of $ \kappa $-Hilfer fractional derivative. The existence and uniqueness results are obtained using Krasnoselskii and Banach's fixed point theorems. We analyze different types of stability results of the proposed problem by using some mathematical methodologies. At the end of the paper, we present a numerical example to demonstrate and validate our findings.

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