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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Solving Nonlinear Integro-Differential Equations Using Numerical Method, Nedjem Eddine Ramdani, Sandra Pinelas
Solving Nonlinear Integro-Differential Equations Using Numerical Method, Nedjem Eddine Ramdani, Sandra Pinelas
Turkish Journal of Mathematics
The aim of this paper is to establish conditions for the existence and uniqueness of the solution of a nonlinear integro-differential equation. Moreover, it is to propose a quadrature method in order to find an approximate solution and establish the convergence of the method. We conclude by providing the algorithm and some numerical simulation to confirm our theoretical results.
Ulam's Type Stability Analysis Of Fractional Difference Equation With Impulse: Gronwall Inequality Approach, Rabia Ilyas, Mujeeb Ur Rehman
Ulam's Type Stability Analysis Of Fractional Difference Equation With Impulse: Gronwall Inequality Approach, Rabia Ilyas, Mujeeb Ur Rehman
Turkish Journal of Mathematics
In this paper, we present a new Gronwall inequality with an impulsive effect. The existence and uniqueness of the solution is investigated through fixed point theorems. Moreover, with the help of newly developed inequality Ulam's type stability criterion is developed for impulsive fractional difference equation. At last, a model is given to help the hypothetical outcome.