Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach

Yaseen M., Mumtaz S., George R., Hussain A.

Fractal and Fractional, vol.6, no.1, 2022 (SCI-Expanded, SSCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 6 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.3390/fractalfract6010017
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, INSPEC, Directory of Open Access Journals
  • Keywords: Caputo-Hadamard fractional derivative, Caputo-Hadamard fractional integral, Hybrid Caputo-Hadamard fractional differential equation and inclusion, Thermostat modeling
  • Uşak University Affiliated: No

Abstract

In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.