Electron. J. Diff. Equ., Vol. 2014 (2014), No. 39, pp. 1-10.

Mild solutions for multi-term time-fractional differential equations with nonlocal initial conditions

Edgardo Alvarez-Pardo, Carlos Lizama

We prove the existence of mild solutions for the multi-term time-fractional order abstract differential equation
 D_t^{\alpha+1} u(t) + c_1 D_t^{\beta_1} u(t)+\dots +c_d {D}_t^{\beta_k} u(t)
 = Au(t) + D_t^{\alpha-1} f(t,u(t)), \quad t\in [0,1],
with nonlocal initial conditions, where A is the generator of a strongly continuous cosine function, $ 0 < \alpha \leq \beta_d \leq \dots \leq \beta_1 \leq 1$ and $ c_k \geq 0$ for $ k=1,\dots ,d$.

Submitted August 28, 2013. Published February 5, 2014.
Math Subject Classifications: 34A08, 35R11, 47D06, 45N05.
Key Words: Multi-term time-fractional differential equation; fractional calculus; cosine operator function; mild solution.

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Edgardo Alvarez-Pardo
Universidad del Atlántico
Facultad de Ciencias Básicas, Departamento de Matemáticas
Barranquilla, Colombia
email: edgardoalvarez@uniatlantico.edu.co, edgalp@yahoo.com
Carlos Lizama
Universidad de Santiago de Chile, Facultad de Ciencia
Departamento de Matemática y Ciencia de la Computación
Casilla 307, Correo 2, Santiago, Chile
email: carlos.lizama@usach.cl

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