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An Extended Analytical and Numerical Study the Nonlocal Boundary Value Problem for the Functional Integro-Differential Equation with the Different Conditions

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Abstract

In this work, we present a study of the nonlocal functional integro-differential equation with the nonlocal conditions. This study is different from the rest of the previous studies as we do the analytical study by studying the existence and uniqueness of the solution and also the continuous dependence of the proposed system. In addition, we apply all results of the analytical studying to some examples and find the exact solutions for them using the modified decomposition method. Also, we offer a numerical study of this system, unless it has been previously studied for the method of solving the proposed examples numerically using the finite difference-Simpson’s method. Some comparisons of numerical solutions are given with exact solutions to show the accuracy of the methods used, in addition to some figures that illustrate this.

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Acknowledgements

All authors thank the editor-in-chief of the journal and all those in charge of it.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt

    K. R. Raslan, Khalid K. Ali & Reda Gamal Ahmed

  2. October High Institute for Engineering and Technology, 6th of October City, Egypt

    Amira Abd-Elall Ibrahim

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  1. K. R. Raslan
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  2. Khalid K. Ali
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  4. Amira Abd-Elall Ibrahim
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If we look at the contribution of each author in this paper, we will find that each of them participated in the work from beginning to end in equal measure.

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Correspondence to Reda Gamal Ahmed.

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Raslan, K.R., Ali, K.K., Ahmed, R.G. et al. An Extended Analytical and Numerical Study the Nonlocal Boundary Value Problem for the Functional Integro-Differential Equation with the Different Conditions. Int. J. Appl. Comput. Math 8, 70 (2022). https://doi.org/10.1007/s40819-022-01269-6

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