SOLUTION OF SECOND AND THIRD ORDER LINEAR DIFFERENTIAL EQUATIONS BY FRACTIONAL CALCULUS

Main Article Content

B. AL-SAQABI
S. L. KALLA

Abstract




The method of fractional calculus is used to obtain particular solutions of some second and third order linear differential equations. Corresponding homogeneous equations are considered. Some results given recently by Nishimoto and Nishimoto & kalla follow as particular cases of our theorems.




Article Details

How to Cite
AL-SAQABI , B., & KALLA, S. L. (1990). SOLUTION OF SECOND AND THIRD ORDER LINEAR DIFFERENTIAL EQUATIONS BY FRACTIONAL CALCULUS. Tamkang Journal of Mathematics, 21(3), 191–200. https://doi.org/10.5556/j.tkjm.21.1990.4658
Section
Papers

References

K. B. Oldha.m and J. Spanier. The Fractional Calculus, Academic Press, New York, 1974.

B. Ross (Editor). Fractional Calculus, Research Notes in Math # 457, Springer-Verlag, 1975.

K. Nishimoto, Fractional Calculus. Descartes Press, Koriyama, Japan, 1984.

A. C. McBride and G.F.Roach(Editors), Fractional Calculus, Pitman, London, 1985.

K. Nishimoto. Fractional Calculus, Vol.II, Descartes Press, Koriyama, Japan 1987.

M. Saigo. A remark on integral operators involving the Gauss' hypergeometric functions. Math. Rep. College General Ed. Kyushu Univ. 11(1978), 135-143.

S. L. Kalla. Operators of fractional integration, In "Analytic Functions": Kozubnik, 1979, Lecture Notes in Mathematics # 798, Springer-Verlag.

I. H. Dimovski and V. S. Kiryakova. Transmutations, Convolutions and fractional powers of Bessel-Type operators via Meijer's G-function. Proc. Complex Anal. and appl., Varna 1985, 45-66.

V. S. Kiryakova. Generalized Operators of Fractional Integration & Differentiation and Applications. Doctoral dissertationa, Inst. Math., Bulgarin Acad. Sci. Sofia, 1987.

S. L. Kalla and B. Ross. The development of functional relations by means of fractional operators. In "Fractional Calculus", Pitman London, 1985.

S. L. Kalla and B. Al-Saqabi. A functional relation involving psi-function. Rev. Tee., Univ. Zulia, 8(ii), 1985, p.31-35.

K. Nishimoto. Application of fractional calculus to the solutions of linear second order differential. equations of Fuchs type, In "Fractional Calculus", Pitman, London, 1985, p.140-153.

K. Nishimoto. An application of fractional calculus to the nonhomogeneous Gauss' equation. Jour. Coll. Eng. Nihon Univ. B-28 (1987), p.1-8.

K. Nishimoto. Fractional calculous and its applications to the non-homogeneous Gauss' equations., Rev. Tee., Univ. Zulia, Vol.IO, no.I, Edicion Especial, 1987.

K. Nishimoto and S.L. Kalla. Use of fractional calculus to solve certain linear differential equations. Jour. Coll. Engg., Nihon univ.