ON THE APPLICATION OF SEQUENTIAL AND FIXED-POINT METHODS TO FRACTIONAL DIFFERENTIAL EQUATIONS OF ARBITRARY ORDER

摘要

This article analyzes the existence and ap-proximation of solutions to initial value problems for nonlin-ear fractional differential equations of arbitrary order. Sev-eral new approaches are furnished in the environment of frac-tional differential equations, such as the sequential technique of Cauchy-Peano and the Leray-Schauder topological degree. In addition, some well-known ideas are optimized in the con-text of Banach's fixed-point theorem. A general version of Gronwall's inequality is also established. A recurring theme throughout the work is the incorporation of desirable quali-ties of the classical Mittag-Leffler function. A YouTube video presentation by the author designed to complement this work is available at http://tinyurl.com/Tisdell-JIEA.