Djamal Foukrach, Soufyane Bouriah, Mouffak Benchohra, Johnny Henderson

Periodic Solutions for Nonlinear Volterra-Fredholm Integro-Differential Equations with ψ-Caputo Fractional Derivative

abstract:
In the present paper, by using the coincidence degree theory of Mawhin introduced in [R.E. Gaines and J.L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations. Lecture Notes in Mathematics, Vol. 568. Springer-Verlag, Berlin-New York, 1977], we discuss the existence and uniqueness of periodic solutions to a large class of problems for a nonlinear Volterra-Fredholm integro-differential equation involving the ψ-Caputo fractional derivative. Two examples are given to substantiate the validity of our findings.

Mathematics Subject Classification: 34A08, 34A12, 34B40, 45J05

Key words and phrases: ψ-Caputo fractional derivative, existence, uniqueness, periodic solutions, coincidence degree theory, Volterra-Fredholm integro-differential equation