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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
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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.
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Solution of Linear Differential Equations With Constant Coefficient
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Non-Sequential Linear Differential Equations with Constant Coefficients
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Systems of Equations Associated with Riemann-Louvilleand Caputo Derivatives
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Solution of Fractional Differential Equations withVariable Coefficients. Generalized Method of Frobenius
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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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References - Podlubny,I.: Fractional Dierential Equations Academic Press, San Diego,
1999. - Samko,G.,Kilbas,A.A., and Marichev,O.I.: Fractional integrals and
deriva-tives: Theory and Applications. Gordon and Breach, Yverdon. 1993.
- Kilbas,A. A.,Srivastava, H. M. and Trujillo,J. J.: Theory and Applicationsof Fractional Dierential Equations, (North-Holland Mathematics Studies).204, 2006.
- Magin, R. L. Fractional Calculus in Bioengineering. Begell House Inc.,Redding, CT, 2006.
- Hilfer, R. (Ed.), Applications of Fractional Calculus in Physics. WorldScientic, Singapore,2000.
- Mainardi, F.:Fractional Calculus and Waves in Linear Viscoelasticity: AnIntroduction to Mathematical Models, (Imperial College Press, London),2010.
- Diethelm, K.:The analysis of fractional dierential equations, Lecture notesin mathematics, Springer,London,2010.