SOME RESULTS ON NONLINEAR FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH POSITIVE CONSTANT COEFFICIENT

Document Type : Regular research papers

Authors

1 Department of Mathematics KBCNMU, Jalgaon

2 Department of Mathematics, N. B. Navale Sinhgad College of Engineering, Kegaon, Solapur

Abstract

In this paper, we study the main results of existence and uniqueness of solutions of fractional Volterra integrodifferential equation involving Caputo fractional derivative of special class $n − 1 < \alpha \leq n, n > 1$. Also, uniqueness of solutions without the existence part and estimate on the solution were discussed. Furthermore, the various type of dependency of solutions of the proposed problem have been studied such as dependence on given initial data, continuously depends on the functions involved in the right side of the problem and on real parameters. The result of existence and uniqueness is obtained with help of well known Banach contraction principle and the integral inequality established by B. G. Pachpatte which provides explicit bound on the unknown function. Authors considered a class of special equations where singularities are removed and we are free to use general integral inequalities to discuss the various properties of solutions. This study may be the new motivation towards the class of more general type.The obtained some results are illustrated through example.

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