Investigating a Class of Pantograph Differential Equations Under Multi-points Boundary Conditions with Fractional Order

Abstract

Qualitative theory for fractional order pantograph differential equations is given in this manuscript. The concerned theory is developed via using some tools of nonlinear analysis along with fixed point results. Some adequate conditions are established for obtaining at least one solution and its existence to the subject to multi-point boundary conditions for problem under consideration. Further, various kinds of Ulam stability results for the solution for the proposed problem are also investigated. To demonstrate our results, some pertinent examples are given.