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

Yaseen, Muhammad; Mumtaz, Sadia; George, Reny; Hussain, AZHAR

doi:10.3390/fractalfract6010017

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, cilt.6, sa.1, 2022 (SCI-Expanded, SSCI, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 6 Sayı: 1
Basım Tarihi: 2022
Doi Numarası: 10.3390/fractalfract6010017
Dergi Adı: Fractal and Fractional
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, INSPEC, Directory of Open Access Journals
Anahtar Kelimeler: Caputo-Hadamard fractional derivative, Caputo-Hadamard fractional integral, Hybrid Caputo-Hadamard fractional differential equation and inclusion, Thermostat modeling
Uşak Üniversitesi Adresli: Hayır

Özet

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.