From Newton's equation to fractional diffusion and wave equations.
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
Similarity:
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
Similarity:
Debnath, Lokenath (2003)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Atanackovic, Teodor, Stankovic, Bogoljub (2007)
Fractional Calculus and Applied Analysis
Similarity:
Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05 We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations...
Stojanović, Mirjana (2011)
Fractional Calculus and Applied Analysis
Similarity:
MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo We generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of...
Branislav Martić (1973)
Publications de l'Institut Mathématique
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...
Marwan Alquran, Kamel Al-Khaled, Mohammed Ali, Omar Abu Arqub (2017)
Waves, Wavelets and Fractals
Similarity:
The Hirota-Satsuma model with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified system is analyzed analytically using a new technique called residual power series method. We observe thatwhen the value of memory index (time-fractional order) is close to zero, the solutions bifurcate and produce a wave-like pattern.
Ayoub, N., Alzoubi, F., Khateeb, H., Al-Qadi, M., Hasan (Qaseer), M., Albiss, B., Rousan, A. (2006)
Fractional Calculus and Applied Analysis
Similarity:
Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05 We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution...
B. Stanković (2011)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Similarity: