Numerical solution of multi-order fractional differential equations using generalized triangular function operational matrices

• Present article proposes numerical technique for the solution of linear and nonlinear multi-order fractional differential equations.
• The proposed method is based on newly computed generalized triangular function operational matrices for Riemann–Liouville fractional order integral.
• Theoretical error analysis is performed to estimate the upper bound of absolute error between the exact Riemann–Liouville fractional order integral and its approximation in the triangular functions domain.

Most fractional differential equations do not have closed form solutions. Development of effective numerical techniques has been an interesting research topic for decades. In this context, this paper proposes a numerical technique, for solving linear and nonlinear multi-order fractional differential equations, based on newly computed generalized triangular function operational matrices for Riemann–Liouville fractional order integral. The orthogonal triangular functions are evolved from a simple dissection of piecewise constant orthogonal block pulse functions. Theoretical error analysis is performed to estimate the upper bound of absolute error between the exact Riemann–Liouville fractional order integral and its approximation in the triangular functions domain. Numerical examples are considered for investigating the applicability and effectiveness of proposed technique to solve multi-order fractional differential equations. The results encourage the use of orthogonal TFs for analysis of real processes exhibiting fractional dynamics.