sequential linear differentional equations of fractional order instructor : v. dr. scientist dumitru...

SEQUENTIAL LINEAR DIFFERENTIONAL EQUATIONS OF FRACTIONAL ORDER

Instructor : V. Dr. Scientist Dumitru BALEANU Seda ERGENÇ - Gözde PARLAK

Çankaya University

Department of Mathematics and Computer Science10.06.2011

Introduction

Fractional calculus is the branch of calculus that generalizes the derivative of a function to non-integer order. The main aim of this project is to understand the theoretical aspects of the sequential fractional derivative and we investigate some illustrative examples. The following topics were investigated: equential linear differential equations of fractional order, solution of linear differential equations with constant coefficients, solutions of fractional differential equations with variable coefficients. For each topic a number of examples were explained.

Solution of Linear Differential Equations With Constant Coefficient

Non-Sequential Linear Differential Equations with Constant Coefficients

Systems of Equations Associated with Riemann-Louvilleand Caputo Derivatives

Solution of Fractional Differential Equations withVariable Coefficients. Generalized Method of Frobenius

Conclusion

In this project , we investigated the sequential linear differential equations of fractional order,solution of linear differential equations with constant coefficients,solutions of fractional differential equations with variable coefficients. We had a view of applications of the theory of the linear differential equations of fractional order. To conclude , we would like to thank Dumitru Baleanu for offering us this subject and for his personal efforts for our senior year Project.

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