Djamal Foukrach, Soufyane Bouriah, Mouffak Benchohra, Johnny Henderson
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