Theoretical and computational results for implicit nonsingular hybrid fractional differential equation subject to multiterms nonlocal initial conditions
Authors
Shafiullah
 Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan.
K. Shah
 Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan.
 Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
M. Sarwar
 Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan.
 Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
Th. Abdeljawad
 Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
Abstract
This research work is devoted to investigate a class of hybrid fractional differential equations with \(n+1\) terms initial conditions. The aforesaid problem is considered under the AtanganaBaleanueCaputo fractional order derivative. Here it is remarkable that hybrid differential equations with linear perturbations have significant applications in modeling various dynamical problems. Sufficient conditions are established for the existence and uniqueness of solution to the problem under investigation by using the Banach and Krasnoselsikii's fixed point theorems. Since stability theory plays important role in establishing various numerical and optimizations results, therefore, HyersUlam type stability results are deduced for the considered problems using the tools of nonlinear functional analysis. Additionally, a numerical method based on Euler procedure is established to study some approbation results for the proposed problem. By a pertinent example, we demonstrate our results. Also some graphical illustrations for different fractional orders are given.
Share and Cite
ISRP Style
Shafiullah, K. Shah, M. Sarwar, Th. Abdeljawad, Theoretical and computational results for implicit nonsingular hybrid fractional differential equation subject to multiterms nonlocal initial conditions, Journal of Mathematics and Computer Science, 36 (2025), no. 2, 207217
AMA Style
Shafiullah, Shah K., Sarwar M., Abdeljawad Th., Theoretical and computational results for implicit nonsingular hybrid fractional differential equation subject to multiterms nonlocal initial conditions. J Math Comput SCIJM. (2025); 36(2):207217
Chicago/Turabian Style
Shafiullah,, Shah, K., Sarwar, M., Abdeljawad, Th.. "Theoretical and computational results for implicit nonsingular hybrid fractional differential equation subject to multiterms nonlocal initial conditions." Journal of Mathematics and Computer Science, 36, no. 2 (2025): 207217
Keywords
 AtanganaBaleanu Caputo derivative
 HyersUlam stability
 fixed point theorem
 Euler numerical method
MSC
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