Investigation of the solvability of $ n $- term fractional quadratic integral equation in a Banach algebra

Hind H. G. Hashem; Asma Al Rwaily; Hind H. G. Hashem; Asma Al Rwaily

doi:10.3934/math.2023146

AIMS Mathematics

2023, Volume 8, Issue 2: 2783-2797. doi: 10.3934/math.2023146

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Research article

Investigation of the solvability of $ n $- term fractional quadratic integral equation in a Banach algebra

Hind H. G. Hashem ¹,
Asma Al Rwaily ^{2
,
,}

1.
Department of mathematics, Faculty of Science, Alexandria University, Alexandria 21544, Egypt
2.
Department of mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Received: 19 September 2022 Revised: 28 October 2022 Accepted: 03 November 2022 Published: 10 November 2022
MSC : 34A08, 34A38, 34A12

In this paper, we consider a nonlinear $ n $-term fractional quadratic integral equation. Our investigation is located in the space $ \; C(J, \; \mathbb{R}).\; $ We prove the existence and uniqueness of the solution for that problem by applying some fixed point theorems. Next, we establish the continuous dependence of the unique solution for that problem on some functions. Finally, we present some particular cases for $ n $-term fractional quadratic integral equation and an example to illustrate our results.
- multi-term quadratic integral equation,
- existence and uniqueness results,
- continuous dependency
Citation: Hind H. G. Hashem, Asma Al Rwaily. Investigation of the solvability of $ n $- term fractional quadratic integral equation in a Banach algebra[J]. AIMS Mathematics, 2023, 8(2): 2783-2797. doi: 10.3934/math.2023146

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Abstract

In this paper, we consider a nonlinear $ n $-term fractional quadratic integral equation. Our investigation is located in the space $ \; C(J, \; \mathbb{R}).\; $ We prove the existence and uniqueness of the solution for that problem by applying some fixed point theorems. Next, we establish the continuous dependence of the unique solution for that problem on some functions. Finally, we present some particular cases for $ n $-term fractional quadratic integral equation and an example to illustrate our results.

References

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