Fractional Integration and Certain Dual Integral Equations.
Roop Narain Kesarwani (1967)
Mathematische Zeitschrift
Similarity:
Roop Narain Kesarwani (1967)
Mathematische Zeitschrift
Similarity:
G. H., and J.E.Littlewood, Hardy (1932)
Mathematische Zeitschrift
Similarity:
G. H., und J. Hardy, J. E. Littlewood (1928)
Mathematische Zeitschrift
Similarity:
R.K. Saxena (1967)
Mathematische Zeitschrift
Similarity:
Roop Narain Kesarwani (1968)
Mathematische Zeitschrift
Similarity:
Krishna Ji Srivastava (1957)
Mathematische Zeitschrift
Similarity:
Branislav Martić (1973)
Publications de l'Institut Mathématique
Similarity:
Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi (2019)
Applications of Mathematics
Similarity:
We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error...
C. Martínez, M.D. Martínez, M. Sanz (1994)
Mathematische Zeitschrift
Similarity:
Li-Li Liu, Jun-Sheng Duan (2015)
Open Mathematics
Similarity:
In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case...
Gülçin Bozkurt, Durmuş Albayrak, Neşe Dernek (2019)
Applications of Mathematics
Similarity:
We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for...