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Numerical analysis of a new volterra integro-differential equation involving fractal-fractional operators

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  • ARAZ, Seda İĞRET

Abstract

In this paper, we suggest a new integro-differential equation by utilizing from the concept of fractal-fractional derivative and integral newly introduced by Atangana. We offer that under which conditions the solution of the suggested equation is exist and unique benefitting from Banach fixed-point theorem. Also, we construct a new numerical scheme for the numerical solution of our problem and we give numerical simulation and illustrations for different values of fractional order α and fractal order β. That’s why, this study will guide for researchers significantly in theory and applications.

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  • ARAZ, Seda İĞRET, 2020. "Numerical analysis of a new volterra integro-differential equation involving fractal-fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303315
    DOI: 10.1016/j.chaos.2019.109396
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    References listed on IDEAS

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    1. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    2. Murat SUBASI & Seda Igret ARAZ & Hakki GUNGOR, 2017. "On the Numerical Solution of Two Dimensional Schrodinger Equation," International Journal of Mathematics Research, Conscientia Beam, vol. 6(1), pages 1-12.
    3. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    4. Atangana, Abdon & Alqahtani, Rubayyi T., 2018. "New numerical method and application to Keller-Segel model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 14-21.
    5. Murat SUBAŞI & Seda İğret ARAZ & Hakkı GÜNGÖR, 2017. "On the Numerical Solution of Two Dimensional Schrodinger Equation," International Journal of Mathematical Research, Conscientia Beam, vol. 6(1), pages 1-12.
    6. Atangana, Ernestine, 2019. "New insight kinetic modeling: Models above classical chemical mechanic," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 16-24.
    7. Chen, W., 2006. "Time–space fabric underlying anomalous diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 923-929.
    8. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
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    Cited by:

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    3. Mallika Arjunan, M. & Hamiaz, A. & Kavitha, V., 2021. "Existence results for Atangana-Baleanu fractional neutral integro-differential systems with infinite delay through sectorial operators," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
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    5. Shojaeizadeh, T. & Mahmoudi, M. & Darehmiraki, M., 2021. "Optimal control problem of advection-diffusion-reaction equation of kind fractal-fractional applying shifted Jacobi polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    7. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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