Two hybrid and non-hybrid k-dimensional inclusion systems via sequential fractional derivatives

Abstract

Some complicated events can be modeled by systems of differential equations. On the other hand, inclusion systems can describe complex phenomena having some shocks better than the system of differential equations. Also, one of the interests of researchers in this field is an investigation of hybrid systems. In this paper, we study the existence of solutions for hybrid and non-hybrid k-dimensional sequential inclusion systems by considering some integral boundary conditions. In this way, we use different methods such as α-ψ contractions and the endpoint technique. Finally, we present two examples to illustrate our main results.

Undetermined Coefficients Method for Sequential Fractional Differential Equations

“…Additionally, in [13], the solution of Equation ( 1) is considered for 𝑛 = 2 and 𝑓(𝑡) = 0. We refer the reader to the papers [14][15][16][17][18][19][20] for some recent work on this subject.…”