OPERATIONAL METHOD FOR THE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH GENERALIZED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES
By Rudolf Hilfer, Yury F. Luchko, Ž. Tomovski. 2009
363 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/6db93fd412db2d5fb26185cd6762fc66c1246961
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Tursun K. Yuldashev
- Bakhtiyor J. Kadirkulovich
- Roberto Garra
- Mohammed D. Kassim
- Federico Polito
- Nasser-Eddine Tatar
- Myong-Ha Kim
- Guk-Chol Ri
Citations in the corpus
- Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions (2018, unknown): “(see [16], Lemma 13) For 0 ≤ γ < 1 and f ∈ Cγ [J,R], then (I 0+f)(0) := lim t→0+ I 0+f(t) = 0, 0 ≤ γ < α.”
- On some operators involving Hadamard derivatives (2013, background): “[8], Luchko and Gorenflo [11], Garra and Polito [6], Tomovski et al.”
- Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives (2013, methodology): “The authors of [6] considered initial values dependent on the type of generalized Riemann-Liouville fractional derivatives in n-term linear fractional differential equation (see problem (36)-(37) in [6]) and defined the space of solutions dependent on the type (see Definition 1 in [6]).”
- NONLOCAL PROBLEM FOR A MIXED TYPE FOURTH-ORDER DIFFERENTIAL EQUATION WITH HILFER FRACTIONAL OPERATOR (2020, methodology): “Based on the results of [12], the authors of [15] have developed an operational method for solving fractional differential equations containing a finite linear combination of the generalized Riemann–Liouville operators with various parameters.”
- Existence and uniqueness for a problem involving Hilfer fractional derivative (2012, background): “Models based on this derivatives are considered in [2,3,7,15].”
- Existence uniqueness and stability of mild solutions for semilinear ψ-Caputo fractional evolution equations (2020, background): “There is variation in the definition of fractional differential operators found in the literature, including Riemann–Liouville, Caputo, Hilfer, Riesz, Erdelyi–Kober, and Hadamard [2, 36] operators.”