On a General Integro Differential Equation with
Parameter

A.M.A. EL-Sayed; M.Sh. Mohamed; A. Basheer

doi:https://doi.org/10.14445/22315373/IJMTT-V68I2P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 2 | Year 2022 | Article Id. IJMTT-V68I2P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I2P509

On a General Integro Differential Equation with Parameter

A.M.A. EL-Sayed, M.Sh. Mohamed, A. Basheer

Abstract

In this paper, we study the existence of solutions 𝑥 for an initial value problem of a general implicit differential equation with parameter in the two classes 𝑥 ∈ 𝐶 1 [0, 𝑇] and 𝑥 ∈ 𝐴𝐶[0, 𝑇]. The maximal and minimal solution will be proved. The uniqueness of the solution will be proved. The continuous dependence of the unique solution will be studied.

Keywords

Implicit differential equation, Continuous solution, Integrable solution, Existence of solutions, Continuous dependence, Maximal and minimal solution.

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Citation :

A.M.A. EL-Sayed, M.Sh. Mohamed, A. Basheer, "On a General Integro Differential Equation with Parameter," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 2, pp. 52-60, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I2P509