Affiliations: [a] Department of Mathematics, Periyar University, Salem, India | [b] Departamento de Análisis Matemático, Facultad de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain | [c] Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia | [d] Department of Mathematics, Erode Sengunthar Engineering College, Erode, India | [e] Department of Mathematics, Central University of Tamil Nadu, Thiruvarur, India
Correspondence:
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Correspondence author: P. Prakash, Department of Mathematics, Periyar University, Salem - 636011, India. Tel.: +91427 2345766/254; Fax: +91427 2345124; [email protected]
Abstract: We consider initial value problems for differential equations of fractional order with uncertainty and present the theory and some numerical methods to solve such type of problems under generalized differentiability conditions. The main tool is Banach fixed point theorem. Also we study the numerical approximation of the solutions of a fuzzy fractional initial value problem by using product trapezoidal and product rectangle formulas; the convergence of the numerical scheme is analyzed rigorously. Finally some numerical examples are provided to illustrate the applicability and usefulness of the obtained results.
Keywords: Fuzzy fractional initial value problem, Banach fixed point theorem, Product trapezoidal rule, Product rectangle rule
