About a new nonlinear integro-differential equation of Volterra-Strum-Liouville type with a weakly singular kernel

Djaafer Mezhoud; Meryem Benssaad; Samir Lemita; Ammar Khellaf

doi:10.5269/bspm.63648

Djaafer Mezhoud National Polytechnic College of Constantine https://orcid.org/0000-0001-6689-8712
Meryem Benssaad Higher Normal School Of Technological Education https://orcid.org/0000-0002-4219-7943
Samir Lemita Normal School of Ouargla https://orcid.org/0000-0003-2568-2493
Ammar Khellaf National Polytechnic College of Constantine https://orcid.org/0000-0001-5282-7593

Abstract

This present paper proposes an analytical and numerical study of a new integro-differential Volterra-Strum-Liouville equation of the second type, having a weak singularity. We provide conditions that guarantee the existence and uniqueness of the solution of the nonlinear problem. Then, we develop a numerical technique using the production integration method. The numerical application shows the efficiency of the proposed procedure.

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