Abstract
We investigate the existence of solutions for a sum-type fractional integro-differential problem via the Caputo differentiation. By using the shifted Legendre and Chebyshev polynomials, we provide a numerical method for finding solutions for the problem. In this way, we give some examples to illustrate our results.
Highlights
In, Reinermann investigated some problems by using approximate fixed point property ([ ])
There has been published some work about different fractional integro-differential equations by using Chebyshev polynomials ([, ] and [ ]) or by using Legendre wavelets ([ – ] and [ ])
In this paper by using an approximate fixed point result and the shifted Legendre and Chebyshev polynomials, we investigate the existence of solutions for a sum-type fractional integro-differential problem
Summary
In , Reinermann investigated some problems by using approximate fixed point property ([ ]). There has been published some work about different fractional integro-differential equations by using Chebyshev polynomials ([ , ] and [ ]) or by using Legendre wavelets ([ – ] and [ ]). In this paper by using an approximate fixed point result and the shifted Legendre and Chebyshev polynomials, we investigate the existence of solutions for a sum-type fractional integro-differential problem. The fractional differential equation cDqx(t) = v(t) has a solution in the form x(t) = Iqv(t) + c + c t + · · · + cn– tn– .
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