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Ming-Fan Li, Ji-Rong Ren, and Tao Zhu., Fractional Vector Calculus and Fractional Special Function // Mathematical Physics.2010. arXiv:1001.2889 [math-ph]



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Ming-Fan Li, Ji-Rong Ren, and Tao Zhu., Fractional Vector Calculus and Fractional Special Function // Mathematical Physics.2010. arXiv:1001.2889 [math-ph].


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    ILOVALAR.


    function Aziz;

    %o'zgarmaslarni qiymatlari


    C0=0.01; Da=1e-6; Vm=1e-4; Dm=1e-5;


    n=50; m=40;
    aa=0.1; bb=0.5;
    tetf=1.0; teta=0.6;
    tau=1;
    h1=0.035;

    tmax=3600;


    bet1=1;
    bet=2;

    %boshlang'ich va chegaraviy shart


    Ca(1:n,1:m,1:tmax)=0;


    Cim(1:n,1:tmax)=0;
    Cm(1:n,1:tmax)=0;
    Cm(1,1:tmax)=C0;
    Ca(1:n,1,1)=Cm(1:n,1);
    Vf=(aa*aa)/(bb*bb);
    Va=1-Vf;
    tetm=Vf*tetf
    tetim=Va*teta
    h2=(bb-aa)/m;

    for k=1:tmax-1


    for i=1:n
    Ca(i,1,k)=Cm(i,k);
    for j=2:m-1
    if (2*bet1)==2
    s0=Ca(i,j+1,k)-2*Ca(i,j,k)+Ca(i,j-1,k);
    else
    s0=0;
    for l=1:j-1
    s0=s0+((l-1+1)^(2-2*bet1)-(l-1)^(2-2*bet1))*(Ca(i,j+2-l,k)-2*Ca(i,j+1-l,k)+Ca(i,j-l,k));
    end;
    end;
    Ca(i,j,k+1)=Ca(i,j,k)+tau*Da/((j*h2)^bet1)*(((j+1/2)^bet1-bet1*(j-1/2)^bet1)/gamma(2-bet1)*...
    (Ca(i,j,k)-bet1*Ca(i,j-1,k))/(gamma(2-bet1)*h2^bet1)+...
    (j*h2)^bet1/(gamma(3-2*bet1)*h2^(2*bet1))*s0);
    end;
    Ca(i,m,k+1)=Ca(i,m-1,k+1);
    Ca(i,1,k+1)=Cm(i,k);

    end;
    q1(k)=-Da*((Ca(1,2,k)-bet1*Ca(1,1,k)))/(gamma(2-bet1)*h2^bet1);


    q2(k)=-Da*((Ca(4,2,k)-bet1*Ca(4,1,k)))/(gamma(2-bet1)*h2^bet1);
    q3(k)=-Da*((Ca(10,2,k)-bet1*Ca(10,1,k)))/(gamma(2-bet1)*h2^bet1);
    A1(k)=Cm(1,k);
    A2(k)=Cm(4,k);
    A3(k)=Cm(6,k);
    A4(k)=Cm(11,k);
    B1(k)=Cim(1,k);
    B2(k)=Cim(4,k);
    B3(k)=Cim(6,k);
    B4(k)=Cim(11,k);
    for i=1:n
    ff=h2/2*(0*Ca(i,1,k+1)+(bb-aa)*Ca(i,m,k+1));
    for j=1:m-1
    ff=ff+h2*(0+j*h2)*Ca(i,j,k+1);
    end;
    Cim(i,k+1)=2*ff/((bb-aa)^2-0);
    end;
    tet=tetim/tetm;
    % G0=gamma(2-gam)*tau^gam;
    D=tau*Dm/(gamma(3-bet)*h1^bet);
    Cm(1,k)=C0;
    for i=2:n-1
    if bet==2
    s0=Cm(i+1,k)-2*Cm(i,k)+Cm(i-1,k);
    else
    s0=0;
    for l=1:i-1
    s0=s0+((l-1+1)^(2-bet)-(l-1)^(2-bet))*(Cm(i+2-l,k)-2*Cm(i+1-l,k)+Cm(i-l,k));
    end;
    end;
    Cm(i,k+1)=D*s0-tau*Vm/h1*(Cm(i,k)-Cm(i-1,k))-tet*(Cim(i,k+1)-Cim(i,k))+Cm(i,k);
    end;
    Cm(n,k+1)=Cm(n-1,k+1);
    k
    end;

    %plot((0:l)*h2,Ca(1:l1,tmax,1:l1));


    %Ca(1:n,tmax-1,1:l1);
    mesh((0:m-1)*h1,(0:m-1)*h2,Ca(1:m,1:m,tmax-1)'),
    set(gca,'FontSize',12);
    % Cim(1:n,tmax/2);
    %Cim(1:n,900)
    %Cim(1:n,1800)
    %Cim(1:n,3600)
    filename1 = 'q1.xlsx';
    sheet = 1;
    xlRange = 'A1';
    xlswrite(filename1,q1',sheet,xlRange);
    xlRange = 'B1';
    xlswrite(filename1,q2',sheet,xlRange);
    xlRange = 'C1';
    xlswrite(filename1,q3',sheet,xlRange);
    filename2 = 'Caa.xlsx';
    xlswrite(filename2,Ca(1:n,1:m,tmax-1));
    filename3 = 'A.xlsx';
    sheet = 1;
    xlRange = 'A1';
    xlswrite(filename3,A1',sheet,xlRange);
    xlRange = 'B1';
    xlswrite(filename3,A2',sheet,xlRange);
    xlRange = 'C1';
    xlswrite(filename3,A3',sheet,xlRange);
    xlRange = 'D1';
    xlswrite(filename3,A4',sheet,xlRange);
    filename4 = 'B.xlsx';
    sheet = 1;
    xlRange = 'A1';
    xlswrite(filename4,B1',sheet,xlRange);
    xlRange = 'B1';
    xlswrite(filename4,B2',sheet,xlRange);
    xlRange = 'C1';
    xlswrite(filename4,B3',sheet,xlRange);
    xlRange = 'D1';
    xlswrite(filename4,B4',sheet,xlRange);
    %Cm(1:n,900)
    %Cm(1:n,1800)
    Cm(1:n,3600)
    hold on;



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