2024/01/30 by H. Ben Brahim, Brahim, Hamza Ben, Fatima-Zahrae El Alaoui +5
Mathematics · Medicine · #35A01 #35R11 #46B50 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2402.01754
openalex publication_date 2024/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the existence and uniqueness of mild solutions for a specific class of time-fractional ψ-Caputo evolution systems with a derivative order ranging from 1 to 2 in Banach spaces. By using the properties of cosine and sine family operators, along with the generalized Laplace transform, we derive a more concise expression for the mild solution. This expression is formulated as an integral, incorporating Mainardi's Wright-type function. Furthermore, we provide various valuable properties associated with the operators present in the mild solution. Additionally, employing the fixed-point technique and Grönwall's inequality, we establish the existence and uniqueness of the mild solution. To illustrate our results, we conclude with an example of a time-fractional equation, presenting the expression for its corresponding mild solution.