Investigating Jerk Phenomenon by Using Fractal-fractional Analysis
Year: 2025
Type: article
Abstract: Fractal-fractional calculus has attracted much attention in the last few years due to its wide range applications in various disciplines of science and technology. The class of differential equations with order lying in [Formula: see text] has significant importance in physics because the concerned equations are usually used to represent jerk or jolt-type phenomenon in real-world applications. Therefore, we consider a class of fractal-fractional differential equations with fractional order [Formula: see text] and fractals dimension [Formula: see text]. The mentioned problem involves proportional-type delay term called Pantograph. We also develop the existence and stability theory for the problem under our consideration using fractal-fractional Riemann–Liouville differential operator. On using the fixed point approach due to Schaefer’s and Banach’s, we investigate appropriate conditions for the existence of at least one solution and its unique. In addition, the Hyers–Ulam ([Formula: see text]) approach of stability is used for stability analysis. Keeping in mind the importance of numerical analysis, Haar wavelets procedure is used to compute some numerical results for the considered problem. Finally, the established results are applied to a numerical problem to explain its validity. Hence, various graphical results related to different fractals and fractional orders have been presented.
Source: Fractals
Institutions: Prince Sultan University, University of Malakand, University of Peshawar, National Yunlin University of Science and Technology, Gulf University for Science & Technology, China Medical University, Sefako Makgatho Health Sciences University, Kyung Hee University, Princess Nourah bint Abdulrahman University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410818697