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Keywords:
mixed Riemann-Liouville fractional derivative; function space concerning fractional derivative; existence and uniqueness; positive solution; fixed point theorem
mixed Riemann-Liouville fractional derivative; function space concerning fractional derivative; existence and uniqueness; positive solution; fixed point theorem
Summary:
Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.
References:
[1] S. G. Samko, A. A. Kilbas, O. I. Marichev: Integrals and Derivatives of Fractional Order and Their Applications. Tekhnika, Minsk, 1987. (Russian) MR 0915556
[2] Osama L. Moustafa: On the Cauchy problem for some fractional order partial differential equations. Chaos, Solitons, Fractals 18 (2003), 135–140. DOI 10.1016/S0960-0779(02)00586-6 | MR 1984554
[3] A. N. Kochubei: A Cauchy problem for evolution equations of fractional order. Differential Equations 25 (1989), 967–974. MR 1014153
[4] A. V. Pshu: Solutions of a boundary value problem for a fractional partial differential equation. Differential Equations 39, 8 (2003), 1150–1158. DOI 10.1023/B:DIEQ.0000011289.79263.02 | MR 2198241
[5] A. N. Vityuk, A. V. Golushkov: Existence of solutions of systems of partial differential equations of fractional order. Nonlinear Oscillations 7 (2004 2004), 318–325. DOI 10.1007/s11072-005-0015-9 | MR 2151816
[6] Domenico Delbosco: Fractional calculus and function spaces. Journal of Fractional Calculus 6 (1994), 45–53. MR 1301228
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