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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 Science 10.06.2011

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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 Solution of Linear Differential Equations With Constant Coefficient

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Non-Sequential Linear Differential Equations with Constant Coefficients Non-Sequential Linear Differential Equations with Constant Coefficients

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Systems of Equations Associated with Riemann-Louville and Caputo Derivatives

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Solution of Fractional Differential Equations with Variable Coefficients. Generalized Method of Frobenius

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Conclusion 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 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 Applications of 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. World Scientic, Singapore,2000. - Mainardi, F.:Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, (Imperial College Press, London), 2010. - Diethelm, K.:The analysis of fractional dierential equations, Lecture notes in mathematics, Springer,London,2010.

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