A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel
Tayyaba Akram, Zeeshan Ali, Faranak Rabiei, Kamal Shah, Poom Kumam
Abstract
Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.
Topics & Concepts
MathematicsKernel (algebra)Stability (learning theory)Nonlinear systemPartial differential equationConvergence (economics)Collocation (remote sensing)Integro-differential equationFractional calculusApplied mathematicsReliability (semiconductor)Differential equationOrder (exchange)Mathematical analysisFirst-order partial differential equationComputer sciencePhysicsCombinatoricsEconomicsPower (physics)Machine learningEconomic growthQuantum mechanicsFinanceFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNumerical methods for differential equations