The Existence of a Positive Solution for a Nonlinear Fractional Differential Equation

By Shuqin Zhang. 2000

270 citations recorded by the source corpus.

We prove existence and uniqueness theorems for a nonlinear fractional differential equation.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e4a7ce118d0edfae73b6b720a4777a295a825b3c

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In Applied Mathematics

1. Zhanbing Bai
2. Ferhan Merdivenci Atici
3. Paul W. Eloe
4. Christopher S. Goodrich
5. Tingting Qiu
6. Varsha Daftardar-Gejji
7. Norazak Senu
8. Mohammed S. Mechee

In Computational Theory and Mathematics

1. Ebene Mboumi
2. Varsha Daftardar-Gejji
3. Zhanbing Bai
4. Khaled M. Furati
5. Rabha W. Ibrahim
6. Paul W. Eloe
7. Shurong Sun
8. Norazak Senu

In Control and Systems Engineering

1. Ebene Mboumi
2. Varsha Daftardar-Gejji
3. Zhanbing Bai
4. Khaled M. Furati
5. Rabha W. Ibrahim
6. Paul W. Eloe
7. Shurong Sun
8. Norazak Senu

Citations in the corpus

• EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS (2008, methodology): “Recently, Zhang [11] considered the existence of positive solution for equation D 0+u = f(t, u), where 0 < α < 1, and f : [0, 1]× [0,+∞) → [0,+∞), is a given continuous function, by using the sub-and super-solution method.”
• Positive solutions for boundary value problem of nonlinear fractional differential equation (2005, unknown): “), see [2, 3, 5, 11, 12].”
• Two-point boundary value problems for finite fractional difference equations (2011, methodology): “We refer the reader to [13–15] for accounts of the historical development; we refer the reader to [4,5,8,16] for samples of recent studies in boundary value problems for fractional differential equations.”
• Existence of positive solutions of nonlinear fractional differential equations (2003, background): “Recently Zhang [1] has addressed the question of existence of positive solutions for the nonlinear fractional equation D s u = f (x, u), u(0) = 0, 0 s 1, 0 x 1, where D s denotes Riemann–Liouville fractional derivative.”
• GENERALIZED ULAM-HYERS STABILITY FOR FRACTIONAL DIFFERENTIAL EQUATIONS (2012, background): “The existence of positive solution and multi-positive solutions for nonlinear fractional differential equation are established and studied [30].”
• Power-type estimates for a nonlinear fractional differential equation (2005, background): “[15], Kilbas and Saigo [17], Tazali [36] and Zhang [37] to cite but a few (see also Kilbas and Trujillo [19] and the references therein).”