Mu, J.; Yuan, Z.; Zhou, Y. Mild Solutions of Fractional Integrodifferential Diffusion Equations with Nonlocal Initial Conditions via the Resolvent Family. Fractal Fract.2023, 7, 785.
Mu, J.; Yuan, Z.; Zhou, Y. Mild Solutions of Fractional Integrodifferential Diffusion Equations with Nonlocal Initial Conditions via the Resolvent Family. Fractal Fract. 2023, 7, 785.
Mu, J.; Yuan, Z.; Zhou, Y. Mild Solutions of Fractional Integrodifferential Diffusion Equations with Nonlocal Initial Conditions via the Resolvent Family. Fractal Fract.2023, 7, 785.
Mu, J.; Yuan, Z.; Zhou, Y. Mild Solutions of Fractional Integrodifferential Diffusion Equations with Nonlocal Initial Conditions via the Resolvent Family. Fractal Fract. 2023, 7, 785.
Abstract
The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.
Keywords
Fractional integro-differential diffusion equations; Nonlocal initial conditions; Resolvent family; Probability density function
Subject
Computer Science and Mathematics, Mathematics
Copyright:
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