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Soft Numerical Algorithm with Convergence Analysis for Time-Fractional Partial IDEs Constrained by Neumann Conditions

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Fractional Calculus (ICFDA 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 303))

Abstract

Some scientific pieces of research are governed by classes of partial integro-differential equations (PIDEs) of fractional order that are leading to novel challenges in simulation and optimization. In this chapter, a soft numerical algorithm is proposed and analyzed to fitted analytical solutions of PIDEs with appropriate initial and Neumann conditions in Sobolev space. Meanwhile, the solutions are represented in series form with strictly computable components. By truncating n-term approximation of the analytical solution, the solution methodology is discussed for both linear and nonlinear problems based on the nonhomogeneous term. Analysis of convergence and smoothness are given under certain assumptions to show the theoretical structures of the method. Dynamic features of the approximate solutions are studied through an illustrated example. The yield of numerical results indicates the accuracy, clarity, and effectiveness of the proposed algorithm as well as provide a proper methodology in handling such fractional issues.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, The University of Jordan, Amman, 11942, Jordan

    Omar Abu Arqub & Shaher Momani

  2. Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun, 26816, Jordan

    Mohammed Al-Smadi

  3. Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman, UAE

    Shaher Momani

Authors
  1. Omar Abu Arqub
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  2. Mohammed Al-Smadi
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  3. Shaher Momani
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Corresponding author

Correspondence to Omar Abu Arqub .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, Rajasthan, India

    Praveen Agarwal

  2. Department of Mathematics and Computer Science, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. School of Engineering (MESA Lab), University of California, Merced, Merced, CA, USA

    YangQuan Chen

  4. Department of Mathematics, The University of Jordan, Amman, Jordan

    Shaher Momani

  5. Institute of Engineering, Polytechnic Institute of Porto, Porto, Portugal

    José António Tenreiro Machado

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Arqub, O.A., Al-Smadi, M., Momani, S. (2019). Soft Numerical Algorithm with Convergence Analysis for Time-Fractional Partial IDEs Constrained by Neumann Conditions. In: Agarwal, P., Baleanu, D., Chen, Y., Momani, S., Machado, J. (eds) Fractional Calculus. ICFDA 2018. Springer Proceedings in Mathematics & Statistics, vol 303. Springer, Singapore. https://doi.org/10.1007/978-981-15-0430-3_7

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