10.1007/s40096-024-00525-8

Analysis of multi-term time complex fractional diffusion equation with Hilfer-Hadamard fractional derivative

  • Pratibha Verma*1,
  • Surabhi Tiwari2,
  1. Department of Mathematics, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, 342030, IN
  2. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, Uttar Pradesh, 211004, IN

Published 2024-10-28

How to Cite

Verma, P., & Tiwari, S. (2024). Analysis of multi-term time complex fractional diffusion equation with Hilfer-Hadamard fractional derivative. Mathematical Sciences, 18(4 (December 2024). https://doi.org/10.1007/s40096-024-00525-8
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Abstract

Abstract This work deals with some new results for existence, uniqueness, and Ulam-Hyers types of stability of the solution of multi-term time complex fractional diffusion equation using Hilfer-Hadamard fractional derivative. We prove the existence and uniqueness of the solution by employing Schaefer’s fixed point theorem and Banach fixed point theorem. Further, we present Ulam-Hyers type stability of the solution of multi-term time complex fractional diffusion equation. Moreover, we discuss the boundedness and interchange properties of the Hilfer-Hadamard fractional operator.

Keywords

  • Complex fractional derivatives,
  • Hilfer-Hadamard fractional derivative,
  • Fixed point theorems,
  • Existence,
  • Uniqueness,
  • Hyers-Ulam stability

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