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The existeness and uniqueness result of solutions to initial value problems of nonlinear diffusion equations involving with the conformable variable derivative

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, based on the conformable derivative, we introduce the concept of conformable variable order derivative. The conformable derivative is a local operator, it has many properties like usual integer derivative’s ones. Similar to the conformable derivative, we study some properties of the conformable variable order derivative. We investigate the fundamental solutions to initial value problem for linear homogeneous and inhomogeneous diffusion differential equations with the conformable variable order derivative. In addition, using upper and lower solutions and monotone iterative method, we consider the existence and uniqueness of solutions to an initial value problem for nonlinear diffusion differential equations involving with the conformable variable order derivative.

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Authors and Affiliations

  1. Department of Mathematics, China University of Mining and Technology, Beijing, 100083, People’s Republic of China

    Shuqin Zhang & Shanshan Li

  2. School of Science, Shandong Jiaotong University, Jinan, 250357, People’s Republic of China

    Lei Hu

Authors
  1. Shuqin Zhang
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  2. Shanshan Li
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  3. Lei Hu
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Correspondence to Shuqin Zhang.

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This research is supported by the Natural Science Foundation of China (11671181)

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Zhang, S., Li, S. & Hu, L. The existeness and uniqueness result of solutions to initial value problems of nonlinear diffusion equations involving with the conformable variable derivative. RACSAM 113, 1601–1623 (2019). https://doi.org/10.1007/s13398-018-0572-2

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  • DOI: https://doi.org/10.1007/s13398-018-0572-2

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