A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method

In this work, the existence and uniqueness solution of the fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position and time-space  L2Ω×C0,T, T<1. The FrNMIoDE conformed to the Volterra-Hammerstein integral equation (V...

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Bibliographic Details
Published inFractal and fractional Vol. 7; no. 9; p. 656
Main Authors Jan, A. R., Abdou, M. A., Basseem, M.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2023
Subjects
Banach spaces
Calculus
Differential equations
discontinuous kernel
Fractional calculus
fractional nonlinear (linear) integro-differential equation
Integral equations
Kernels
Mathematical analysis
Methods
nonlinear algebraic system
Nystrom method
Quadratures
the rate of convergence error
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Summary:In this work, the existence and uniqueness solution of the fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position and time-space  L2Ω×C0,T, T<1. The FrNMIoDE conformed to the Volterra-Hammerstein integral equation (V-HIE) of the second kind, after applying the characteristics of a fractional integral, with a general discontinuous kernel in position for the Hammerstein integral term and a continuous kernel in time to the Volterra integral (VI) term. Then, using a separation technique methodology, we developed HIE, whose physical coefficients were time-variable. By examining the system’s convergence, the product Nystrom technique (PNT) and associated schemes were employed to create a nonlinear algebraic system (NAS).
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7090656