@Thomas Richard
 M1.mw

@Thomas Richard thanks for your response.. It is working, but I have an error when tried to ploting

y(x):=eA(t).B+int(v(x)*eA(x-t)*theta(t-x),0..1);

You have any possiblities to solve this issue....

@Carl Love Thank you for your response. Your comments are very useful... I got a result

proc(x_bvp)  ...  end;
sol(0);
print(`output redirected...`); # input placeholder
                             sol(0)

But cannot get a solution How to find a solution.

It is possible to solve this equations to any other numerical method?

I used infinity = 10, but result is

Error, (in dsolve/numeric/bvp) Newton iteration is not converging

@C_R Thak you for your response...

The expression of equation has been rewritten by

((D@@2)(theta))(eta) = -(-D[t]*epsilon*(-gamma+beta)*(D(theta))(eta)+beta*(D[B]*epsilon*(mu-lambda)*(D(phi))(eta)+(1/2)*nu*(f(eta)*sin(alpha)+eta*cos(alpha))))*(D(theta))(eta)/(beta*sigma)

and removed the extra argument

Le = nu/D[B]

How to simplify this problem?

@Rouben Rostamian  Thank you for your response....

I attached my worksheet with correct form of equatons and initial and boundary conditons.

Kindly solve this...PDE_system.mw

@Carl Love Great thank for you....

Respected @Kitonum, hear alpha is an arbitrary angle and the boundary conditions are;

f(x) tends to 0;
g(x) tends to b;
h(x) tends to c;

for x tends to infinity, where b and c are some constants

Lot of thanks @Kitonum ...

Is it possible to find a values of unknown variables a1, a2 and a3?

@tomleslie thankyou for your commands.

This plots are not working in Maple 18. Please, can you solve this problem.

@Kitonum thank you very much.
How to plot these absolute abs ()?

@Kitonum is it possible to find exact initial conditions of the DE for the curve is convergence?

Thank you @Kitonum  sir... its very useful