SOME RESULTS ON NONLINEAR MIXED FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

H. L.Tidke; V. V.Kharat; G. N.More

H. L.Tidke Department of Mathematics, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, India
V. V.Kharat Department of Mathematics, N. B. Navale Sinhgad College of Engineering, Kegaon, Solapur, India
G. N.More Department of Mathematics, Y. C. Institute of Science, Satara, India

Article ID: 2567

Keywords: fractional mixed integrodifferential equation; existence and uniqueness of solution; fixed point theorem; integral inequality

Abstract

In this paper, we study the existence, uniqueness and other properties of solutions of fractional Volterra Fredholm integrodifferential equation involving Caputo fractional derivative of special class $n-1<\alpha \leq n, \quad n>1$. The result of existence and uniqueness is obtained with help of well known Banach contraction principle and the integral inequality which provides explicit bound on the unknown function. The obtained some results are illustrated through example.

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