Nonlinear fractional differential equations and their existence via fixed point theory concerning to Hilfer generalized proportional fractional derivative-Reference-Cited by-同舟云学术

Nonlinear fractional differential equations and their existence via fixed point theory concerning to Hilfer generalized proportional fractional derivative

Published:2023 Issue:1 Volume:8 Page:382-403
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Rashid Saima¹,Ahmad Abdulaziz Garba²,Jarad Fahd³⁴⁵,Alsaadi Ateq⁶

Affiliation:

1. Department of Mathematics, Government College University, Faisalabad, Pakistan

2. Department of Mathematics Programme, National Mathematical Centre, Abuja, Nigeria

3. Department of Mathematics, Çankaya University, Ankara, Turkey

4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

5. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

6. Department of Mathematics and Statistics, College of Science, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia

Abstract

<abstract><p>This article adopts a class of nonlinear fractional differential equation associating Hilfer generalized proportional fractional ($ GPF $) derivative with having boundary conditions, which amalgamates the Riemann-Liouville $ (RL) $ and Caputo-$ GPF $ derivative. Taking into consideration the weighted space continuous mappings, we first derive a corresponding integral for the specified boundary value problem. Also, we investigate the existence consequences for a certain problem with a new unified formulation considering the minimal suppositions on nonlinear mapping. Detailed developments hold in the analysis and are dependent on diverse tools involving Schauder's, Schaefer's and Kransnoselskii's fixed point theorems. Finally, we deliver two examples to check the efficiency of the proposed scheme.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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