THERMAL SCIENCE
International Scientific Journal
DISCRETE FRACTIONAL SOLUTION OF A NONHOMOGENEOUS NON-FUCHSIAN DIFFERENTIAL EQUATIONS
ABSTRACT
In this article, we also present new fractional solutions of the non-homogeneous and homogeneous non-Fuchsian differential equation by using nabla-discrete fractional calculus operator α(0 < α < 1). So, we acquire new solution of these equation in the discrete fractional form via a newly developed method.
KEYWORDS
PAPER SUBMITTED: 2018-09-17
PAPER REVISED: 2018-11-03
PAPER ACCEPTED: 2018-11-15
PUBLISHED ONLINE: 2018-12-16
THERMAL SCIENCE YEAR
2019, VOLUME
23, ISSUE
Supplement 1, PAGES [S121 - S127]
- Miller, K.S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, Inc., New York, 1993
- Oldham, K., Spanier, J., The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Dover Publications, Inc., Mineola, New York, 2002
- Podlubny, I., Fractional Differential Equations, Academic Press, New York, New York, 1999
- Sabatier, J., et al., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, 2007
- Samko, G., et al., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993
- Kuttner, B., On differences of fractional order, Proceeding of the London Mathematical Society, 3 (1957), pp. 453-466
- Diaz J.B., Osler, T.J., Differences of Fractional Order, American Mathematical Society, 28 (1974), pp. 185-202
- Atıcı, F.M., Eloe, P.W., A transform method in discrete fractional calculus, International Journal of Difference Equations, 2 (2007), pp. 165-176
- Atıcı, F.M., Eloe, P.W., Initial value problems in discrete fractional calculus, Proceeding of the American Mathematical Society, 137 (2009), pp. 981-989
- Atıcı, F.M., Eloe, P.W., Discrete fractional calculus with the nabla operator, Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed I, 3 (2009), pp. 1-12
- Atıcı, F.M., Eloe, P.W., Two-point boundary value problems for nite fractional difference equations, J. Difference Equations and Applications, 17 (2011), pp. 445-456
- Acar, N., Atıcı, F.M., Exponential functions of discrete fractional calculus, Appl. Anal. Discrete Math., 7 (2013), pp. 343-353
- Yilmazer,R., Ozturk, O.,On Nabla Discrete Fractional Calculus Operator for a Modified Bessel Equation, Thermal Science, 22 (1) (2018), pp. S203-S209
- Yilmazer, R., et al, Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator. Entropy, 18 (2016), 49, pp. 1-6
- Abdeljawad, T., Atıcı, F.M., On the Definitions of Nabla Fractional Operators. Abstr. Appl. Anal., (2012), Article ID 406757, 13 pages
- Wu, G.C., Baleanu, D., Discrete fractional logistic map and its chaos, Nonlinear Dyn., 75 (2014), pp. 283-287
- Atıcı, F.M., Sengül, S., Modeling with fractional difference equations, J. Math. Anal. Appl., 369 (2010), pp. 1-9
- Mohan, J.J., Solutions of perturbed nonlinear nabla fractional difference equations, Novi Sad. J. Math., 43 (2013), pp. 125-138
- Mohan, J.J., Analysis of nonlinear fractional nabla difference equations, Int. J. Analysis Applications, 7 (2015), pp. 79-95
- Yilmazer, R., N-fractional calculus operator N method to a modified hydrogen atom equation, Math. Commun., 15 (2010), pp. 489-501
- Yang, C., Liu, W., Zhou, Q., Mihalache, D., Malomed, B.A., One-soliton shaping and twosoliton interaction in the fifth-order variable-coefficient nonlinear Schrödinger equation, Nonlinear Dynamics, 92 (2) (2018), pp. 203-213
- Zhou, Q., Sonmezoglu, A., Ekici, M. and Mirzazadeh, M., Optical solitons of some fractional differential equations in nonlinear optics, Journal of Modern Optics, 64 (21) (2017), pp. 2345-2349
- Zubair, A., Raza, N., Mirzazadeh, M., Liu, W., Zhou, Q., Analytic study on optical solitons in parity-time-symmetric mixed linear and nonlinear modulation lattices with non-Kerr nonlinearities, Optik, 173 (2018), pp. 249-262
- Granger, C. W. J., Joyeux, R., An introduction to long-memory time series models and fractional differencing, J. Time Ser. Anal., 1 (1980), pp. 15-29
- Hosking, J. R. M., Fractional differencing, Biometrika, 68 (1981), pp. 165-176
- Gray, H.L., Zhang, N., On a New Definition of the Fractional Difference, Mathematics of Computation, 50 (182) (1988), pp. 513-529
- Anastassiou, G.A., Nabla discrete fractional calculus and nabla inequalities, Mathematical and Computer Modelling, 51 (2010), pp. 562 - 571
- Kelley, W. G., Peterson, A. C., Difference Equations: An Introduction with Applications. Academic Press, San Diego, 2001