Fractional calculus and fractional differential equations (Master thesis)

Καππέ, Αντωνία

In this Msc Thesis we are concerned with fractional calculus and problems related to fractional differential equations. We introduce fractional integrals and fractional derivatives as defined by Riemann-Liouville, Caputo, Grunwald-Letnikov, Erdelyi-Kober and Hadamard. We study some properties of Riemann-Liouville fractional derivatives and we quote some applications to problems in Mathematics and Physics. Subsequently, we deal with fractional order differential equations of Riemann-Liouville type. More specifically, we solve initial value problems for linear differential equations of fractional order. We deal with the existence and uniqueness of solutions of non-linear differential equations of fractional order in spaces of continuous as well as in spaces of integrable functions. Moreover, we examine how the solution of a fractional differential equation depends on the order of the equation and the initial value problems. We are also concerned with an initial value problem of a delayed differential equation of fractional order. Last, we study the existence of a solution to a two-point boundary value problem as well as to a multipoint eigenvalue problem.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών
Subject classification: Κλασματικός λογισμός
Keywords: Κλασματικός λογισμός
Appears in Collections:Διατριβές Μεταπτυχιακής Έρευνας (Masters)

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