A nonlinear fractional partial integro‐differential equation with nonlocal initial value conditions
Copyright policy )A nonlinear fractional partial integro‐differential equation with nonlocal initial value conditions
In this work, we study a new nonlinear partial integro‐differential equation with nonlocal initial value conditions and investigate the solutions of this equation. By considering an equivalent implicit integral equation via series, we prove the uniqueness of solutions of the equation by Babenko's approach, Banach's contraction principle, and the multivariable Mittag–Leffler function. We also demonstrate the application of our key theorem with an illustrative example.
- Czech Academy of Sciences Czech Republic
- University of Galway Ireland
- Iran University of Science and Technology Iran (Islamic Republic of)
- Institute of Information Theory and Automation Czech Republic
- Brandon University Canada
nonlinear partial integro-differential equation, Fractional derivatives and integrals, multivariate Mittag-Leffler function, Integral representations of solutions to PDEs, Banach's contractive principle, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), Fractional partial differential equations, Babenko's approach
nonlinear partial integro-differential equation, Fractional derivatives and integrals, multivariate Mittag-Leffler function, Integral representations of solutions to PDEs, Banach's contractive principle, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), Fractional partial differential equations, Babenko's approach
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