On the analytical and numerical study for fractional q-integrodifferential equations

Boundary Value Problems

Research

Khalid K. Ali¹  K. R. Raslan¹  Afaf A. S. Zaghrout¹  Amira Abd-Elall Ibrahim² 

[1] Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt;October High Institute for Engineering and Technology, Giza, Egypt;

关键词: q;    Existence and uniqueness of solution;    Numerical solutions;   

DOI  :  10.1186/s13661-022-01680-4

 received in 2022-06-19, accepted in 2022-11-26,  发布年份 2022

来源: Springer

【 摘 要 】

In this paper, we give some basic concepts of q-calculus that will be needed in this paper. Then, we built the q-nonlocal condition that ensures the solution existence and uniqueness of the fractional q-integrodifferential equation. Also, we introduce the continuous dependence of the solution. We find the numerical solution using the finite-difference-Trapezoidal and the cubic B-spline-Trapezoidal methods. Finally, we give three examples to illustrate the validity of our main results.

【 授权许可】

CC BY   
© The Author(s) 2022

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