Novel algorithms to approximate the solution of nonlinear integro-differential equations of Volterra-Fredholm integro type

Hawsar HamaRashid; Hari Mohan Srivastava; Mudhafar Hama; Pshtiwan Othman Mohammed; Musawa Yahya Almusawa; Dumitru Baleanu; Hawsar HamaRashid; Hari Mohan Srivastava; Mudhafar Hama; Pshtiwan Othman Mohammed; Musawa Yahya Almusawa; Dumitru Baleanu

doi:10.3934/math.2023745

AIMS Mathematics

2023, Volume 8, Issue 6: 14572-14591. doi: 10.3934/math.2023745

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Novel algorithms to approximate the solution of nonlinear integro-differential equations of Volterra-Fredholm integro type

1.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
2.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
3.
Department of Mathematics and Informatics, Azerbaijan University, AZ1007 Baku, Azerbaijan
4.
Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
6.
Department of Mathematics, College of Science, University of Sulaimani, Sulaimani 46001, Iraq
7.
Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
8.
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
9.
Institute of Space Sciences, R76900 Magurele-Bucharest, Romania
10.
Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut 11022801, Lebanon

Received: 04 February 2023 Revised: 11 April 2023 Accepted: 11 April 2023 Published: 20 April 2023
MSC : 34A45, 34B15, 45J05, 65L10

This study is devoted to examine the existence and uniqueness behavior of a nonlinear integro-differential equation of Volterra-Fredholm integral type in continues space. Then, we examine its solution by modification of Adomian and homotopy analysis methods numerically. Initially, the proposed model is reformulated into an abstract space, and the existence and uniqueness of solution is constructed by employing Arzela-Ascoli and Krasnoselskii fixed point theorems. Furthermore, suitable conditions are developed to prove the proposed model's continues behavior which reflects the stable generation. At last, three test examples are presented to verify the established theoretical concepts.
- boundary value problem,
- Arzela-Ascoli theorem,
- Krasnosel'skii theorem,
- nonlinear integro equation
Citation: Hawsar HamaRashid, Hari Mohan Srivastava, Mudhafar Hama, Pshtiwan Othman Mohammed, Musawa Yahya Almusawa, Dumitru Baleanu. Novel algorithms to approximate the solution of nonlinear integro-differential equations of Volterra-Fredholm integro type[J]. AIMS Mathematics, 2023, 8(6): 14572-14591. doi: 10.3934/math.2023745

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Abstract

This study is devoted to examine the existence and uniqueness behavior of a nonlinear integro-differential equation of Volterra-Fredholm integral type in continues space. Then, we examine its solution by modification of Adomian and homotopy analysis methods numerically. Initially, the proposed model is reformulated into an abstract space, and the existence and uniqueness of solution is constructed by employing Arzela-Ascoli and Krasnoselskii fixed point theorems. Furthermore, suitable conditions are developed to prove the proposed model's continues behavior which reflects the stable generation. At last, three test examples are presented to verify the established theoretical concepts.

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