HYERS-ULAM STABILITY ANALYSIS FOR PIECEWISE VARIABLE ORDER FRACTIONAL IMPULSIVE EVOLUTION SYSTEMS

We investigate a class of piecewise variable-order fractional differential equations with impulsive and nonlocal conditions in Banach space. The nonhomogeneous term in the proposed system is given in terms of variable kernel which has flexibility property. We formulate appropriate equivalent integral equations to the considered evolution problem, then we show the solvability results by using mainly fractional calculus and fixed point techniques. Further, we study Hyers-Ulam stability analysis by adapting suitable conditions. The concerned area has numerous applications in those evolution processes and phenomenon, where abrupt changes occur. At the end, we support our obtained theory by illustrative and computational example.