The existence and uniqueness of solutions to nonlinear ordinary differential equations with fractal-fractional derivatives, with Dirac-delta, exponential decay, power law, and generalized Mittag-Leffler kernels, have been the focus of this work. To do this, we used the Chaplygin approach, which entails creating two lower and upper sequences that converge to the solution of the equations under consideration. We have for each case provided the conditions under which these sequences are obtained and converge.
Citation: Abdon Atangana, Seda İğret Araz. Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations[J]. AIMS Mathematics, 2024, 9(3): 5763-5793. doi: 10.3934/math.2024280
The existence and uniqueness of solutions to nonlinear ordinary differential equations with fractal-fractional derivatives, with Dirac-delta, exponential decay, power law, and generalized Mittag-Leffler kernels, have been the focus of this work. To do this, we used the Chaplygin approach, which entails creating two lower and upper sequences that converge to the solution of the equations under consideration. We have for each case provided the conditions under which these sequences are obtained and converge.
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Abdon Atangana, Seda İğret Araz. Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations[J]. AIMS Mathematics, 2024, 9(3): 5763-5793. doi: 10.3934/math.2024280
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